LMFDB - Embedded newform 324.2.l.a.179.3

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			179.3
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.3

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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	0.106648	−	0.994297i	$-0.465988\pi$
$5$	−0.297855	−	0.0525198i	−0.133205	−	0.0234876i	−0.239853	+	0.970809i	$0.577099\pi$
$6$		0			0
$7$	−0.312070	−	0.371910i	−0.117951	−	0.140569i	0.703838	−	0.710361i	$-0.251468\pi$
$7$	−0.312070	−	0.371910i	−0.117951	−	0.140569i	−0.821789	+	0.569792i	$0.807024\pi$
$8$	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	0.985878	−	0.167464i	$-0.0535577\pi$
$11$	0.00722947	+	0.0410004i	0.00217977	+	0.0123621i	−0.983698	+	0.179826i	$0.942447\pi$
$12$		0			0
$13$	4.05761	−	1.47685i	1.12538	−	0.409604i	0.288765	−	0.957400i	$-0.406755\pi$
$13$	4.05761	−	1.47685i	1.12538	−	0.409604i	0.836612	+	0.547796i	$0.184533\pi$
$14$	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	0.736960	−	0.675936i	$-0.236261\pi$
$17$	2.14427	+	1.23800i	0.520062	+	0.300258i	−0.216898	+	0.976194i	$0.569594\pi$
$18$		0			0
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.503430	−	0.864036i	$-0.332071\pi$
$19$	6.55326	−	3.78353i	1.50342	−	0.868001i	0.999992	−	0.00396479i	$-0.00126203\pi$
$20$	−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	0.993014	−	0.118000i	$-0.0376481\pi$
$23$	5.03199	+	4.22234i	1.04924	+	0.880418i	0.0562281	+	0.998418i	$0.482093\pi$
$24$		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	−0.489231	−	0.872154i	$-0.662722\pi$
$29$	2.40260	−	6.60109i	0.446152	−	1.22579i	0.935383	−	0.353637i	$-0.115055\pi$
$30$		0			0
$31$	2.30836	−	2.75099i	0.414593	−	0.494092i	−0.517819	−	0.855490i	$-0.673256\pi$
$31$	2.30836	−	2.75099i	0.414593	−	0.494092i	0.932412	+	0.361398i	$0.117700\pi$
$32$	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	0.445696	+	0.895184i	$0.352956\pi$
$37$	−3.36015	+	5.81994i	−0.552405	+	0.956793i	−0.998100	+	0.0616082i	$0.980377\pi$
$38$	−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	−0.986011	−	0.166680i	$-0.946695\pi$
$41$	−2.16312	−	5.94312i	−0.337823	−	0.928160i	0.648188	−	0.761480i	$-0.275527\pi$
$42$		0			0
$43$	−2.38200	+	0.420011i	−0.363252	+	0.0640511i	−0.352295	−	0.935889i	$-0.614599\pi$
$43$	−2.38200	+	0.420011i	−0.363252	+	0.0640511i	−0.0109565	+	0.999940i	$0.503488\pi$
$44$	−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	−0.145365	−	0.989378i	$-0.546436\pi$
$47$	5.51016	−	4.62358i	0.803740	−	0.674418i	0.949105	+	0.314960i	$0.101991\pi$
$48$		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	$0.238230\pi$
$53$			9.90799i			1.36097i	−0.732763	+	0.680484i	$0.761770\pi$
$54$		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	0.895236	+	0.445592i	$0.147007\pi$
$59$	−0.755918	+	4.28703i	−0.0984122	+	0.558123i	−0.993648	+	0.112531i	$0.964104\pi$
$60$		0			0
$61$	−5.77142	+	4.84280i	−0.738955	+	0.620057i	−0.932557	−	0.361024i	$-0.882427\pi$
$61$	−5.77142	+	4.84280i	−0.738955	+	0.620057i	0.193602	+	0.981080i	$0.437983\pi$
$62$	−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	0.921354	+	0.388724i	$0.127084\pi$
$67$	3.80965	+	10.4669i	0.465423	+	1.27874i	−0.455932	+	0.890015i	$0.650694\pi$
$68$	−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	−0.948685	−	0.316223i	$-0.897585\pi$
$71$	−1.68932	+	2.92598i	−0.200485	+	0.347250i	0.748200	+	0.663473i	$0.230918\pi$
$72$		0			0
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	0.883897	−	0.467682i	$-0.154911\pi$
$73$	0.315477	+	0.546421i	0.0369237	+	0.0639538i	−0.846973	+	0.531636i	$0.821577\pi$
$74$	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	−0.984214	−	0.176982i	$-0.943367\pi$
$79$	−1.03548	+	2.84496i	−0.116501	+	0.320083i	0.867714	+	0.497065i	$0.165589\pi$
$80$	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	0.0275495	−	0.999620i	$-0.491230\pi$
$83$	−5.41059	−	1.96930i	−0.593890	−	0.216158i	−0.621439	+	0.783462i	$0.713452\pi$
$84$		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	−0.894491	−	0.447085i	$-0.852462\pi$
$89$	−9.00521	+	5.19916i	−0.954550	+	0.551110i	−0.0600588	+	0.998195i	$0.519129\pi$
$90$		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	0.941256	−	0.337694i	$-0.109647\pi$
$97$	−0.578459	−	3.28061i	−0.0587337	−	0.333095i	−0.999989	+	0.00459941i	$0.998536\pi$
$98$	−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	0.960366	+	0.278743i	$0.0899177\pi$
$101$	10.7344	+	12.7927i	1.06811	+	1.27292i	0.107742	+	0.994179i	$0.465638\pi$
$102$		0			0
$103$	−15.6512	−	2.75973i	−1.54216	−	0.271924i	−0.663062	−	0.748565i	$-0.730743\pi$
$103$	−15.6512	−	2.75973i	−1.54216	−	0.271924i	−0.879098	+	0.476640i	$0.841854\pi$
$104$	−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	−0.542997	−	0.839735i	$-0.682710\pi$
$113$	−14.2492	−	2.51252i	−1.34045	−	0.236358i	−0.797456	+	0.603377i	$0.793821\pi$
$114$		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	−0.801200	−	0.598397i	$-0.795805\pi$
$127$	−7.70348	+	4.44760i	−0.683573	+	0.394661i	0.117627	+	0.993058i	$0.462471\pi$
$128$	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	−0.990027	−	0.140881i	$-0.955006\pi$
$131$	−14.8870	−	12.4917i	−1.30068	−	1.09140i	−0.310657	−	0.950522i	$-0.600549\pi$
$132$		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	−0.485834	−	0.874051i	$-0.661484\pi$
$137$	5.24564	−	14.4123i	0.448165	−	1.23132i	0.934000	−	0.357274i	$-0.116294\pi$
$138$		0			0
$139$	5.74324	−	6.84453i	0.487135	−	0.580545i	−0.465351	−	0.885126i	$-0.654072\pi$
$139$	5.74324	−	6.84453i	0.487135	−	0.580545i	0.952486	+	0.304581i	$0.0985164\pi$
$140$	−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	0.913228	−	0.407448i	$-0.133581\pi$
$149$	−0.588938	−	1.61809i	−0.0482477	−	0.132559i	−0.961476	+	0.274889i	$0.911359\pi$
$150$		0			0
$151$	0.593940	−	0.104728i	0.0483342	−	0.00852262i	−0.149429	−	0.988772i	$-0.547743\pi$
$151$	0.593940	−	0.104728i	0.0483342	−	0.00852262i	0.197763	+	0.980250i	$0.436632\pi$
$152$	−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	0.824592	+	0.565729i	$0.191405\pi$
$157$	−1.80133	+	10.2158i	−0.143762	+	0.815313i	−0.968353	+	0.249584i	$0.919706\pi$
$158$	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	$0.0717148\pi$
$163$			5.70430i			0.446795i	−0.974727	+	0.223397i	$0.928285\pi$
$164$	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	−0.928995	−	0.370092i	$-0.879326\pi$
$167$	0.911752	−	5.17080i	0.0705535	−	0.400129i	0.999549	−	0.0300372i	$-0.00956257\pi$
$168$		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	−0.121472	−	0.992595i	$-0.538762\pi$
$173$	1.36617	−	0.240893i	0.103868	−	0.0183148i	0.225341	+	0.974280i	$0.427650\pi$
$174$		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	−0.565591	−	0.824686i	$-0.691352\pi$
$179$	5.77179	−	9.99703i	0.431403	−	0.747213i	0.996994	+	0.0774732i	$0.0246852\pi$
$180$		0			0
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	0.986039	+	0.166514i	$0.0532510\pi$
$181$	8.57298	+	14.8488i	0.637225	+	1.10371i	−0.348814	+	0.937192i	$0.613416\pi$
$182$	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	−0.288933	−	0.957349i	$-0.593300\pi$
$191$	−15.5567	−	5.66216i	−1.12564	−	0.409699i	−0.836708	+	0.547650i	$0.815523\pi$
$192$		0			0
$193$	−6.74355	−	5.65851i	−0.485411	−	0.407308i	0.366967	−	0.930234i	$-0.380396\pi$
$193$	−6.74355	−	5.65851i	−0.485411	−	0.407308i	−0.852378	+	0.522925i	$0.824841\pi$
$194$	−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	−0.0621526	−	0.998067i	$-0.519797\pi$
$197$	10.8232	−	6.24879i	0.771122	−	0.445208i	0.833275	+	0.552859i	$0.186463\pi$
$198$		0			0
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	0.355927	−	0.934514i	$-0.384165\pi$
$199$	−3.88531	−	2.24318i	−0.275422	−	0.159015i	−0.631349	+	0.775499i	$0.717499\pi$
$200$	−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	−0.650570	−	0.759446i	$-0.725470\pi$
$211$	−22.1033	−	3.89740i	−1.52165	−	0.268308i	−0.871082	+	0.491138i	$0.836581\pi$
$212$	−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	0.999281	−	0.0379061i	$-0.0120688\pi$
$223$	11.7737	+	14.0314i	0.788428	+	0.939612i	−0.210854	+	0.977518i	$0.567624\pi$
$224$	−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	0.860888	+	0.508794i	$0.169908\pi$
$227$	3.40406	+	19.3054i	0.225936	+	1.28134i	−0.634953	+	0.772551i	$0.718980\pi$
$228$		0			0
$229$	−5.32626	+	1.93860i	−0.351969	+	0.128106i	−0.511953	−	0.859013i	$-0.671078\pi$
$229$	−5.32626	+	1.93860i	−0.351969	+	0.128106i	0.159984	+	0.987120i	$0.448856\pi$
$230$	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	0.271552	−	0.962424i	$-0.412463\pi$
$233$	−6.50499	−	3.75566i	−0.426156	−	0.246041i	−0.697708	+	0.716383i	$0.745797\pi$
$234$		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	0.788890	−	0.614535i	$-0.210656\pi$
$239$	4.95760	+	4.15992i	0.320680	+	0.269083i	−0.468209	+	0.883618i	$0.655101\pi$
$240$		0			0
$241$	0.652071	+	0.237335i	0.0420036	+	0.0152881i	0.362937	−	0.931814i	$-0.381774\pi$
$241$	0.652071	+	0.237335i	0.0420036	+	0.0152881i	−0.320933	+	0.947102i	$0.603996\pi$
$242$	−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	0.829533	−	0.558457i	$-0.188607\pi$
$251$	−1.09113	−	1.88989i	−0.0688715	−	0.119289i	−0.898405	+	0.439168i	$0.855273\pi$
$252$		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	0.993237	+	0.116102i	$0.0370398\pi$
$257$	4.92162	+	13.5220i	0.307002	+	0.843481i	−0.686235	+	0.727380i	$0.740738\pi$
$258$		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	−0.851829	−	0.523819i	$-0.824507\pi$
$263$	−7.84733	+	6.58469i	−0.483887	+	0.406029i	0.367943	+	0.929849i	$0.380062\pi$
$264$		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	$-0.969364\pi$
$269$		−	3.15222i		−	0.192194i	0.995372	−	0.0960971i	$-0.0306359\pi$
$270$		0			0
$271$			3.33151i			0.202375i	0.994867	+	0.101188i	$0.0322642\pi$
$271$			3.33151i			0.202375i	−0.994867	+	0.101188i	$0.967736\pi$
$272$	−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	−0.541618	−	0.840625i	$-0.682188\pi$
$277$	3.19860	−	2.68395i	0.192186	−	0.161263i	0.733803	+	0.679362i	$0.237743\pi$
$278$	−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	−0.717330	−	0.696733i	$-0.754636\pi$
$281$	−19.3295	+	3.40832i	−1.15310	+	0.203323i	−0.435773	+	0.900057i	$0.643525\pi$
$282$		0			0
$283$	5.26641	+	14.4693i	0.313055	+	0.860113i	0.992036	+	0.125956i	$0.0401999\pi$
$283$	5.26641	+	14.4693i	0.313055	+	0.860113i	−0.678980	+	0.734156i	$0.737578\pi$
$284$	−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	−0.992446	−	0.122683i	$-0.960850\pi$
$293$	−11.9699	+	14.2652i	−0.699290	+	0.833382i	0.293156	+	0.956065i	$0.405295\pi$
$294$		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	0.912136	−	0.409887i	$-0.134432\pi$
$307$	17.7533	+	10.2499i	1.01323	+	0.584990i	0.101096	+	0.994877i	$0.467765\pi$
$308$	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	0.252081	−	0.967706i	$-0.418885\pi$
$311$	18.8205	−	6.85012i	1.06722	−	0.388435i	0.815135	+	0.579272i	$0.196663\pi$
$312$		0			0
$313$	−3.06340	−	17.3734i	−0.173154	−	0.982003i	−0.940253	−	0.340475i	$-0.889412\pi$
$313$	−3.06340	−	17.3734i	−0.173154	−	0.982003i	0.767100	−	0.641528i	$-0.221699\pi$
$314$	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	0.682886	−	0.730525i	$-0.260725\pi$
$317$	−2.76189	−	3.29149i	−0.155123	−	0.184868i	−0.838009	+	0.545657i	$0.816280\pi$
$318$		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	0.282554	−	0.959252i	$-0.408819\pi$
$331$	−12.9390	−	15.4201i	−0.711190	−	0.847563i	−0.993743	+	0.111689i	$0.964374\pi$
$332$	−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	−0.657186	−	0.753728i	$-0.728254\pi$
$337$	−12.4122	+	4.51765i	−0.676133	+	0.246092i	−0.0189468	+	0.999820i	$0.506031\pi$
$338$	−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	0.931277	−	0.364313i	$-0.118696\pi$
$347$	13.6769	+	11.4763i	0.734213	+	0.616078i	−0.197064	+	0.980391i	$0.563141\pi$
$348$		0			0
$349$	12.2841	+	4.47105i	0.657554	+	0.239330i	0.649180	−	0.760635i	$-0.275112\pi$
$349$	12.2841	+	4.47105i	0.657554	+	0.239330i	0.00837388	+	0.999965i	$0.497334\pi$
$350$	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	0.575328	+	0.817923i	$0.304874\pi$
$353$	−7.34903	+	20.1913i	−0.391149	+	1.07467i	−0.966477	+	0.256751i	$0.917348\pi$
$354$		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	1.00000		0.000407927i	$-0.000129847\pi$
$359$	9.46695	+	16.3972i	0.499647	+	0.865413i	−0.500353	+	0.865821i	$0.666797\pi$
$360$		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	0.476236	−	0.879317i	$-0.342001\pi$
$367$	23.4580	−	4.13627i	1.22450	−	0.215912i	0.748260	+	0.663406i	$0.230890\pi$
$368$	−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	0.717705	+	0.696348i	$0.245193\pi$
$373$	−3.76380	+	21.3456i	−0.194882	+	1.10523i	−0.912587	+	0.408883i	$0.865918\pi$
$374$	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	$-0.667338\pi$
$379$		−	33.6783i		−	1.72994i	0.501825	−	0.864969i	$-0.332662\pi$
$380$	−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	−0.977411	−	0.211347i	$-0.932215\pi$
$383$	0.261068	−	1.48059i	0.0133400	−	0.0756548i	0.990751	+	0.135693i	$0.0433260\pi$
$384$		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	−0.0764044	−	0.997077i	$-0.524344\pi$
$389$	3.80299	−	0.670570i	0.192819	−	0.0339993i	0.269224	+	0.963078i	$0.413233\pi$
$390$		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	0.507894	−	0.861419i	$-0.330424\pi$
$397$	−9.80431	−	16.9816i	−0.492064	−	0.852280i	−0.999958	+	0.00913954i	$0.997091\pi$
$398$	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	−0.295788	−	0.955254i	$-0.595582\pi$
$401$	13.9437	−	16.6175i	0.696316	−	0.829838i	0.992104	+	0.125416i	$0.0400266\pi$
$402$		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	0.410286	−	0.911957i	$-0.365429\pi$
$409$	−8.42462	−	7.06909i	−0.416570	−	0.349544i	−0.826857	+	0.562413i	$0.809873\pi$
$410$	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	−0.831635	−	0.555323i	$-0.812595\pi$
$419$	−22.7569	+	8.28284i	−1.11175	+	0.404643i	−0.280114	+	0.959967i	$0.590372\pi$
$420$		0			0
$421$	6.35770	+	36.0563i	0.309855	+	1.75728i	0.599721	+	0.800209i	$0.295278\pi$
$421$	6.35770	+	36.0563i	0.309855	+	1.75728i	−0.289866	+	0.957067i	$0.593611\pi$
$422$	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	0.793305	−	0.608824i	$-0.208359\pi$
$439$	1.17279	+	1.39768i	0.0559744	+	0.0667077i	−0.737331	+	0.675532i	$0.763914\pi$
$440$	−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	0.976764	−	0.214317i	$-0.0687526\pi$
$443$	−0.302973	−	1.71824i	−0.0143947	−	0.0816362i	−0.991159	+	0.132681i	$0.957641\pi$
$444$		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	0.299164	−	0.954202i	$-0.403292\pi$
$449$	−8.00158	−	4.61971i	−0.377618	−	0.218018i	−0.676781	+	0.736184i	$0.736626\pi$
$450$		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	0.867550	−	0.497350i	$-0.165694\pi$
$457$	25.9190	+	9.43376i	1.21244	+	0.441293i	0.344891	+	0.938643i	$0.387916\pi$
$458$	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	0.657737	+	0.753247i	$0.271514\pi$
$461$	−7.09177	+	19.4845i	−0.330297	+	0.907483i	−0.988034	+	0.154236i	$0.950709\pi$
$462$		0			0
$463$	6.16175	−	7.34328i	0.286361	−	0.341271i	−0.603618	−	0.797274i	$-0.706275\pi$
$463$	6.16175	−	7.34328i	0.286361	−	0.341271i	0.889979	+	0.456002i	$0.150719\pi$
$464$	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	0.589516	−	0.807757i	$-0.299319\pi$
$467$	−8.74737	−	15.1509i	−0.404780	−	0.701099i	−0.994296	+	0.106657i	$0.965985\pi$
$468$		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	−0.0565037	−	0.998402i	$-0.517995\pi$
$479$	20.0678	−	16.8388i	0.916919	−	0.769386i	0.973423	+	0.229016i	$0.0735508\pi$
$480$		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	$0.0514986\pi$
$487$			7.10957i			0.322166i	−0.986941	+	0.161083i	$0.948501\pi$
$488$	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	−0.804174	−	0.594393i	$-0.797392\pi$
$491$	3.43007	−	19.4529i	0.154797	−	0.877897i	0.958971	−	0.283503i	$-0.0914967\pi$
$492$		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	0.740591	+	0.671956i	$0.234546\pi$
$499$	13.5189	+	37.1430i	0.605191	+	1.66275i	−0.135400	+	0.990791i	$0.543232\pi$
$500$	−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	−0.0107769	+	0.999942i	$0.503430\pi$
$503$	−19.5426	+	33.8489i	−0.871364	+	1.50925i	−0.860587	+	0.509304i	$0.829903\pi$
$504$		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	−0.513877	−	0.857864i	$-0.671791\pi$
$509$	9.47986	−	11.2977i	0.420187	−	0.500760i	0.934065	+	0.357104i	$0.116236\pi$
$510$		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	−0.261424	−	0.965224i	$-0.584192\pi$
$521$	10.1293	−	5.84816i	0.443773	−	0.256213i	0.705197	+	0.709012i	$0.250859\pi$
$522$		0			0
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	0.341505	−	0.939880i	$-0.389063\pi$
$523$	−6.89969	−	3.98354i	−0.301702	−	0.174188i	−0.643207	+	0.765692i	$0.722397\pi$
$524$	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	0.470309	−	0.882502i	$-0.344142\pi$
$547$	−11.2369	−	13.3916i	−0.480453	−	0.572582i	−0.950763	+	0.309920i	$0.899698\pi$
$548$	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	0.485336	−	0.874328i	$-0.338697\pi$
$557$	−0.688812	−	0.397686i	−0.0291859	−	0.0168505i	−0.514522	+	0.857477i	$0.672031\pi$
$558$		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	0.536017	−	0.844207i	$-0.319928\pi$
$563$	−4.79979	−	4.02750i	−0.202287	−	0.169739i	−0.738304	+	0.674468i	$0.764373\pi$
$564$		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	−0.972462	−	0.233063i	$-0.925125\pi$
$569$	−1.85350	+	5.09244i	−0.0777027	+	0.213486i	0.894759	+	0.446550i	$0.147347\pi$
$570$		0			0
$571$	−19.5951	+	23.3525i	−0.820029	+	0.977273i	−0.999979	−	0.00640314i	$-0.997962\pi$
$571$	−19.5951	+	23.3525i	−0.820029	+	0.977273i	0.179950	+	0.983676i	$0.442406\pi$
$572$	−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	−0.994059	−	0.108843i	$-0.965286\pi$
$577$	−9.67484	+	16.7573i	−0.402769	+	0.697616i	0.591290	+	0.806459i	$0.298619\pi$
$578$	−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	−0.394227	+	0.919013i	$0.628988\pi$
$587$	−33.1376	+	27.8057i	−1.36773	+	1.14767i	−0.973508	+	0.228653i	$0.926568\pi$
$588$		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	$0.235121\pi$
$593$			32.7916i			1.34659i	−0.739375	+	0.673294i	$0.764879\pi$
$594$		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	0.497624	+	0.867393i	$0.334206\pi$
$599$	−6.52625	+	37.0122i	−0.266655	+	1.51228i	−0.764279	+	0.644885i	$0.776905\pi$
$600$		0			0
$601$	7.65033	−	6.41939i	0.312063	−	0.261852i	−0.473281	−	0.880912i	$-0.656930\pi$
$601$	7.65033	−	6.41939i	0.312063	−	0.261852i	0.785344	+	0.619059i	$0.212486\pi$
$602$	−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	−0.960792	−	0.277271i	$-0.910570\pi$
$607$	−9.92909	−	27.2799i	−0.403009	−	1.10726i	0.557783	−	0.829987i	$-0.311652\pi$
$608$	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	0.566866	−	0.823810i	$-0.308156\pi$
$613$	−10.6465	−	18.4402i	−0.430007	−	0.744794i	−0.996873	+	0.0790155i	$0.974822\pi$
$614$	−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	−0.797255	−	0.603642i	$-0.793716\pi$
$617$	−1.59822	+	1.90469i	−0.0643420	+	0.0766798i	0.732913	+	0.680322i	$0.238160\pi$
$618$		0			0
$619$	−4.56324	+	12.5374i	−0.183412	+	0.503921i	−0.996990	−	0.0775360i	$-0.975295\pi$
$619$	−4.56324	+	12.5374i	−0.183412	+	0.503921i	0.813577	+	0.581457i	$0.197517\pi$
$620$	−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	−0.335117	−	0.942176i	$-0.608776\pi$
$631$	−33.1235	−	19.1238i	−1.31862	−	0.761308i	−0.983507	+	0.180868i	$0.942109\pi$
$632$	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	0.554811	−	0.831976i	$-0.312791\pi$
$641$	−9.13644	−	10.8884i	−0.360868	−	0.430065i	−0.915679	+	0.401911i	$0.868346\pi$
$642$		0			0
$643$	−0.627325	−	0.110614i	−0.0247393	−	0.00436221i	0.161265	−	0.986911i	$-0.448443\pi$
$643$	−0.627325	−	0.110614i	−0.0247393	−	0.00436221i	−0.186004	+	0.982549i	$0.559554\pi$
$644$	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	−0.477938	−	0.878393i	$-0.658616\pi$
$653$	−31.3669	−	5.53083i	−1.22748	−	0.216438i	−0.749543	+	0.661955i	$0.769727\pi$
$654$		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	0.993147	+	0.116871i	$0.0372864\pi$
$659$	2.56367	+	14.5393i	0.0998663	+	0.566370i	−0.893281	+	0.449499i	$0.851603\pi$
$660$		0			0
$661$	−18.8308	+	6.85385i	−0.732433	+	0.266584i	−0.681194	−	0.732103i	$-0.738539\pi$
$661$	−18.8308	+	6.85385i	−0.732433	+	0.266584i	−0.0512388	+	0.998686i	$0.516317\pi$
$662$	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	−0.375713	−	0.926736i	$-0.622602\pi$
$673$	−32.6670	−	11.8898i	−1.25922	−	0.458319i	−0.883508	+	0.468417i	$0.844825\pi$
$674$	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	0.496630	+	0.867962i	$0.334571\pi$
$677$	−11.4934	+	31.5778i	−0.441726	+	1.21363i	−0.938356	+	0.345670i	$0.887652\pi$
$678$		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	0.999459	−	0.0329044i	$-0.0104757\pi$
$683$	12.3153	+	21.3308i	0.471233	+	0.816200i	−0.528225	+	0.849104i	$0.677142\pi$
$684$		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	−0.442113	−	0.896960i	$-0.645771\pi$
$691$	−14.4784	+	2.55293i	−0.550784	+	0.0971181i	−0.108672	+	0.994078i	$0.534660\pi$
$692$	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	$-0.790843\pi$
$701$		−	32.3443i		−	1.22163i	0.791775	−	0.610813i	$-0.209157\pi$
$702$		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	−0.999044	−	0.0437162i	$-0.986080\pi$
$709$	−30.0746	+	25.2356i	−1.12947	+	0.947741i	−0.130430	+	0.991458i	$0.541636\pi$
$710$	−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	−0.874878	−	0.484343i	$-0.839059\pi$
$719$	−0.482259	+	0.835298i	−0.0179852	+	0.0311514i	0.856893	+	0.515495i	$0.172392\pi$
$720$		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	0.732892	+	0.680345i	$0.238170\pi$
$727$	−7.16819	+	19.6944i	−0.265854	+	0.730427i	−0.998745	+	0.0500812i	$0.984052\pi$
$728$	−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	0.667829	−	0.744315i	$-0.267224\pi$
$733$	1.37507	+	1.15382i	0.0507892	+	0.0426172i	−0.617040	+	0.786932i	$0.711668\pi$
$734$	−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	0.781017	−	0.624510i	$-0.214701\pi$
$739$	17.1448	+	9.89858i	0.630683	+	0.364125i	−0.150333	+	0.988635i	$0.548035\pi$
$740$	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	0.426721	−	0.904383i	$-0.359669\pi$
$743$	36.3877	−	13.2440i	1.33494	−	0.485877i	0.908214	+	0.418507i	$0.137446\pi$
$744$		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	−0.256716	−	0.966487i	$-0.582641\pi$
$751$	−22.7048	−	4.00346i	−0.828508	−	0.146088i	−0.571792	+	0.820398i	$0.693752\pi$
$752$	−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	−0.117087	−	0.993122i	$-0.537356\pi$
$761$	−15.6353	−	2.75693i	−0.566780	−	0.0999386i	−0.449693	+	0.893183i	$0.648467\pi$
$762$		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	0.0595284	−	0.998227i	$-0.481040\pi$
$769$	20.7088	−	7.53738i	0.746777	−	0.271805i	0.687249	+	0.726422i	$0.258818\pi$
$770$	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	0.800330	−	0.599560i	$-0.204658\pi$
$773$	18.9410	+	10.9356i	0.681261	+	0.393326i	−0.119069	+	0.992886i	$0.537991\pi$
$774$		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	−0.803388	−	0.595456i	$-0.796971\pi$
$787$	−2.17335	+	2.59010i	−0.0774716	+	0.0923271i	0.725916	+	0.687783i	$0.241416\pi$
$788$	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	−0.788679	−	0.614805i	$-0.789235\pi$
$797$	−16.3658	−	44.9646i	−0.579705	−	1.59273i	0.208974	−	0.977921i	$-0.432988\pi$
$798$		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	$0.0987356\pi$
$809$			17.3637i			0.610473i	−0.952277	+	0.305237i	$0.901264\pi$
$810$		0			0
$811$			13.7618i			0.483242i	0.970371	+	0.241621i	$0.0776791\pi$
$811$			13.7618i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$812$	−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	0.304732	−	0.952438i	$-0.401433\pi$
$821$	26.2703	−	4.63216i	0.916840	−	0.161664i	0.612108	+	0.790774i	$0.290322\pi$
$822$		0			0
$823$	−15.0879	−	41.4538i	−0.525932	−	1.44499i	−0.863820	−	0.503801i	$-0.831935\pi$
$823$	−15.0879	−	41.4538i	−0.525932	−	1.44499i	0.337888	−	0.941186i	$-0.390288\pi$
$824$	−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	−0.750436	−	0.660943i	$-0.770157\pi$
$827$	5.67028	−	9.82121i	0.197175	−	0.341517i	0.947611	+	0.319426i	$0.103490\pi$
$828$		0			0
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	0.999985	+	0.00549015i	$0.00174758\pi$
$829$	14.5329	+	25.1717i	0.504747	+	0.874248i	−0.495238	+	0.868757i	$0.664919\pi$
$830$	−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	0.143998	−	0.989578i	$-0.454004\pi$
$839$	−11.0585	−	4.02496i	−0.381781	−	0.138957i	−0.525779	+	0.850621i	$0.676226\pi$
$840$		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	−0.782971	−	0.622058i	$-0.786297\pi$
$853$	−7.59288	−	43.0614i	−0.259975	−	1.47439i	0.522996	−	0.852335i	$-0.324814\pi$
$854$	−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	0.808949	−	0.587879i	$-0.200037\pi$
$857$	2.62091	+	3.12348i	0.0895287	+	0.106696i	−0.719420	+	0.694575i	$0.755592\pi$
$858$		0			0
$859$	38.3251	+	6.75775i	1.30764	+	0.230571i	0.783675	−	0.621171i	$-0.213343\pi$
$859$	38.3251	+	6.75775i	1.30764	+	0.230571i	0.523961	+	0.851743i	$0.324454\pi$
$860$	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	−0.0575935	−	0.998340i	$-0.518343\pi$
$877$	15.9919	−	5.82058i	0.540008	−	0.196547i	0.597602	+	0.801793i	$0.296120\pi$
$878$	−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	0.543095	−	0.839672i	$-0.317252\pi$
$881$	2.59611	+	1.49886i	0.0874651	+	0.0504980i	−0.455630	+	0.890169i	$0.650586\pi$
$882$		0			0
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	−0.184154	−	0.982897i	$-0.558954\pi$
$883$	17.0858	−	9.86450i	0.574984	−	0.331967i	0.759137	+	0.650931i	$0.225621\pi$
$884$	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	0.999711	+	0.0240206i	$0.00764673\pi$
$887$	35.6487	+	29.9128i	1.19697	+	1.00437i	0.197254	+	0.980352i	$0.436798\pi$
$888$		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	0.426954	−	0.904273i	$-0.359587\pi$
$907$	34.2556	−	6.04019i	1.13744	−	0.200561i	0.710485	+	0.703712i	$0.248476\pi$
$908$	−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	−0.938012	−	0.346604i	$-0.887335\pi$
$911$	−22.9255	+	19.2368i	−0.759557	+	0.637344i	0.178454	+	0.983948i	$0.442890\pi$
$912$		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	$-0.663942\pi$
$919$		−	52.7647i		−	1.74055i	0.492569	−	0.870273i	$-0.336058\pi$
$920$	−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	0.827321	−	0.561729i	$-0.189864\pi$
$929$	54.7677	−	9.65703i	1.79687	−	0.316837i	0.969550	+	0.244892i	$0.0787526\pi$
$930$		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	0.975667	−	0.219255i	$-0.0703628\pi$
$937$	9.12048	+	15.7971i	0.297953	+	0.516070i	−0.677715	+	0.735325i	$0.737029\pi$
$938$	−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	−0.917078	−	0.398707i	$-0.869459\pi$
$941$	−11.2021	+	13.3502i	−0.365179	+	0.435204i	0.551899	+	0.833911i	$0.313903\pi$
$942$		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	0.901458	−	0.432868i	$-0.142498\pi$
$947$	40.4292	+	14.7150i	1.31377	+	0.478174i	0.412315	+	0.911042i	$0.364720\pi$
$948$		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	−0.187449	−	0.982274i	$-0.560022\pi$
$953$	17.5809	−	10.1503i	0.569502	−	0.328802i	0.756950	+	0.653472i	$0.226688\pi$
$954$		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	0.854359	−	0.519683i	$-0.173950\pi$
$967$	46.0060	+	8.11209i	1.47945	+	0.260867i	0.625093	+	0.780550i	$0.285061\pi$
$968$	−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	−0.128468	−	0.991714i	$-0.541006\pi$
$977$	−18.3908	−	3.24280i	−0.588375	−	0.103746i	−0.459907	+	0.887967i	$0.652117\pi$
$978$		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	−0.967428	−	0.253148i	$-0.918534\pi$
$983$	−4.54380	−	25.7692i	−0.144925	−	0.821909i	0.822503	−	0.568761i	$-0.192577\pi$
$984$		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	−0.847932	−	0.530105i	$-0.822153\pi$
$991$	−25.5875	+	14.7730i	−0.812815	+	0.469279i	0.0351178	+	0.999383i	$0.488819\pi$
$992$	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	−0.322787	−	0.946472i	$-0.604620\pi$
$997$	−37.2095	−	13.5431i	−1.17844	−	0.428916i	−0.855649	+	0.517556i	$0.826842\pi$
$998$	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.179.3		96
3.2	odd	2		108.2.l.a.23.14	yes	96
4.3	odd	2	inner	324.2.l.a.179.16		96
9.2	odd	6		972.2.l.c.215.8		96
9.4	even	3		972.2.l.a.863.14		96
9.5	odd	6		972.2.l.d.863.3		96
9.7	even	3		972.2.l.b.215.9		96
12.11	even	2		108.2.l.a.23.1	✓	96
27.2	odd	18		972.2.l.a.107.5		96
27.7	even	9		108.2.l.a.47.1	yes	96
27.11	odd	18		972.2.l.b.755.7		96
27.16	even	9		972.2.l.c.755.10		96
27.20	odd	18	inner	324.2.l.a.143.16		96
27.25	even	9		972.2.l.d.107.12		96
36.7	odd	6		972.2.l.b.215.7		96
36.11	even	6		972.2.l.c.215.10		96
36.23	even	6		972.2.l.d.863.12		96
36.31	odd	6		972.2.l.a.863.5		96
108.7	odd	18		108.2.l.a.47.14	yes	96
108.11	even	18		972.2.l.b.755.9		96
108.43	odd	18		972.2.l.c.755.8		96
108.47	even	18	inner	324.2.l.a.143.3		96
108.79	odd	18		972.2.l.d.107.3		96
108.83	even	18		972.2.l.a.107.14		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	12.11	even	2
108.2.l.a.23.14	yes	96	3.2	odd	2
108.2.l.a.47.1	yes	96	27.7	even	9
108.2.l.a.47.14	yes	96	108.7	odd	18
324.2.l.a.143.3		96	108.47	even	18	inner
324.2.l.a.143.16		96	27.20	odd	18	inner
324.2.l.a.179.3		96	1.1	even	1	trivial
324.2.l.a.179.16		96	4.3	odd	2	inner
972.2.l.a.107.5		96	27.2	odd	18
972.2.l.a.107.14		96	108.83	even	18
972.2.l.a.863.5		96	36.31	odd	6
972.2.l.a.863.14		96	9.4	even	3
972.2.l.b.215.7		96	36.7	odd	6
972.2.l.b.215.9		96	9.7	even	3
972.2.l.b.755.7		96	27.11	odd	18
972.2.l.b.755.9		96	108.11	even	18
972.2.l.c.215.8		96	9.2	odd	6
972.2.l.c.215.10		96	36.11	even	6
972.2.l.c.755.8		96	108.43	odd	18
972.2.l.c.755.10		96	27.16	even	9
972.2.l.d.107.3		96	108.79	odd	18
972.2.l.d.107.12		96	27.25	even	9
972.2.l.d.863.3		96	9.5	odd	6
972.2.l.d.863.12		96	36.23	even	6

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

Varieties

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Database

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