LMFDB - Embedded newform 324.2.l.a.143.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(35,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			143.16
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40830 - 0.129170i) q^{2} +(1.96663 - 0.363822i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(0.312070 - 0.371910i) q^{7} +(2.72261 - 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(-0.00722947 + 0.0410004i) q^{11} +(4.05761 + 1.47685i) q^{13} +(0.391449 - 0.564072i) q^{14} +(3.73527 - 1.43101i) q^{16} +(2.14427 - 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.566662 + 0.211653i) q^{20} +(-0.00488525 + 0.0586748i) q^{22} +(-5.03199 + 4.22234i) q^{23} +(-4.61250 + 1.67881i) q^{25} +(5.90510 + 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(2.40260 + 6.60109i) q^{29} +(-2.30836 - 2.75099i) q^{31} +(5.07554 - 2.49778i) q^{32} +(2.85987 - 2.02045i) q^{34} +(-0.0734187 + 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-9.71770 - 4.48186i) q^{38} +(-0.770692 + 0.371267i) q^{40} +(-2.16312 + 5.94312i) q^{41} +(2.38200 + 0.420011i) q^{43} +(0.000699143 + 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(-5.51016 - 4.62358i) q^{47} +(1.17461 + 6.66153i) q^{49} +(-6.27895 + 2.96008i) q^{50} +(8.51712 + 1.42817i) q^{52} -9.90799i q^{53} -0.0125918i q^{55} +(0.564613 - 1.25174i) q^{56} +(4.23625 + 8.98598i) q^{58} +(0.755918 + 4.28703i) q^{59} +(-5.77142 - 4.84280i) q^{61} +(-3.60621 - 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-1.28614 - 0.226781i) q^{65} +(-3.80965 + 10.4669i) q^{67} +(3.76658 - 3.21481i) q^{68} +(-0.0869698 + 0.188570i) q^{70} +(1.68932 + 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(-5.48386 - 7.76221i) q^{74} +(-14.2644 - 5.05658i) q^{76} +(0.0129924 + 0.0154837i) q^{77} +(1.03548 + 2.84496i) q^{79} +(-1.03741 + 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(5.41059 - 1.96930i) q^{83} +(-0.573662 + 0.481360i) q^{85} +(3.40883 + 0.283818i) q^{86} +(0.0117397 + 0.117169i) q^{88} +(-9.00521 - 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(-8.35988 + 10.1345i) q^{92} +(-8.35720 - 5.79964i) q^{94} +(2.15063 + 0.782765i) q^{95} +(-0.578459 + 3.28061i) q^{97} +(2.51468 + 9.22972i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	1.40830	−	0.129170i	0.995820	−	0.0913373i
$2$	1.40830	−	0.129170i	0.995820	−	0.0913373i
$3$		0			0
$3$		0			0
$4$	1.96663	−	0.363822i	0.983315	−	0.181911i
$5$	−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	−0.703838	−	0.710361i	$-0.748532\pi$
$7$	0.312070	−	0.371910i	0.117951	−	0.140569i	0.821789	+	0.569792i	$0.192976\pi$
$8$	2.72261	−	0.766402i	0.962589	−	0.270964i
$9$		0			0
$10$	−0.412685	+	0.112438i	−0.130503	+	0.0355559i
$11$	−0.00722947	+	0.0410004i	−0.00217977	+	0.0123621i	−0.985878	−	0.167464i	$-0.946442\pi$
$11$	−0.00722947	+	0.0410004i	−0.00217977	+	0.0123621i	0.983698	+	0.179826i	$0.0575534\pi$
$12$		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	$0.406755\pi$
$14$	0.391449	−	0.564072i	0.104619	−	0.150755i
$15$		0			0
$16$	3.73527	−	1.43101i	0.933817	−	0.357752i
$17$	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	$-0.998738\pi$
$19$	−6.55326	−	3.78353i	−1.50342	−	0.868001i	−0.503430	−	0.864036i	$-0.667929\pi$
$20$	−0.566662	+	0.211653i	−0.126709	+	0.0473271i
$21$		0			0
$22$	−0.00488525	+	0.0586748i	−0.00104154	+	0.0125095i
$23$	−5.03199	+	4.22234i	−1.04924	+	0.880418i	−0.993014	−	0.118000i	$-0.962352\pi$
$23$	−5.03199	+	4.22234i	−1.04924	+	0.880418i	−0.0562281	+	0.998418i	$0.517907\pi$
$24$		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	0.517819	−	0.855490i	$-0.326744\pi$
$31$	−2.30836	−	2.75099i	−0.414593	−	0.494092i	−0.932412	+	0.361398i	$0.882300\pi$
$32$	5.07554	−	2.49778i	0.897237	−	0.441549i
$33$		0			0
$34$	2.85987	−	2.02045i	0.490464	−	0.346504i
$35$	−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	$-0.352956\pi$
$38$	−9.71770	−	4.48186i	−1.57642	−	0.727054i
$39$		0			0
$40$	−0.770692	+	0.371267i	−0.121857	+	0.0587025i
$41$	−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	0.352295	−	0.935889i	$-0.385401\pi$
$43$	2.38200	+	0.420011i	0.363252	+	0.0640511i	0.0109565	+	0.999940i	$0.496512\pi$
$44$	0.000699143		0.0832628i	0.000105400		0.0125523i
$45$		0			0
$46$	−6.54116	+	6.59631i	−0.964441	+	0.972573i
$47$	−5.51016	−	4.62358i	−0.803740	−	0.674418i	0.145365	−	0.989378i	$-0.453564\pi$
$47$	−5.51016	−	4.62358i	−0.803740	−	0.674418i	−0.949105	+	0.314960i	$0.898009\pi$
$48$		0			0
$49$	1.17461	+	6.66153i	0.167801	+	0.951647i
$50$	−6.27895	+	2.96008i	−0.887977	+	0.418618i
$51$		0			0
$52$	8.51712	+	1.42817i	1.18111	+	0.198051i
$53$		−	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
$56$	0.564613	−	1.25174i	0.0754495	−	0.167271i
$57$		0			0
$58$	4.23625	+	8.98598i	0.556247	+	1.17992i
$59$	0.755918	+	4.28703i	0.0984122	+	0.558123i	0.993648	+	0.112531i	$0.0358958\pi$
$59$	0.755918	+	4.28703i	0.0984122	+	0.558123i	−0.895236	+	0.445592i	$0.852993\pi$
$60$		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	$0.882427\pi$
$62$	−3.60621	−	3.57605i	−0.457989	−	0.454159i
$63$		0			0
$64$	6.82526	−	4.17323i	0.853157	−	0.521654i
$65$	−1.28614	−	0.226781i	−0.159526	−	0.0281287i
$66$		0			0
$67$	−3.80965	+	10.4669i	−0.465423	+	1.27874i	0.455932	+	0.890015i	$0.349306\pi$
$67$	−3.80965	+	10.4669i	−0.465423	+	1.27874i	−0.921354	+	0.388724i	$0.872916\pi$
$68$	3.76658	−	3.21481i	0.456765	−	0.389853i
$69$		0			0
$70$	−0.0869698	+	0.188570i	−0.0103949	+	0.0225385i
$71$	1.68932	+	2.92598i	0.200485	+	0.347250i	0.948685	−	0.316223i	$-0.102415\pi$
$71$	1.68932	+	2.92598i	0.200485	+	0.347250i	−0.748200	+	0.663473i	$0.769082\pi$
$72$		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	$0.154911\pi$
$74$	−5.48386	−	7.76221i	−0.637486	−	0.902338i
$75$		0			0
$76$	−14.2644	−	5.05658i	−1.63624	−	0.580029i
$77$	0.0129924	+	0.0154837i	0.00148062	+	0.00176453i
$78$		0			0
$79$	1.03548	+	2.84496i	0.116501	+	0.320083i	0.984214	−	0.176982i	$-0.0566334\pi$
$79$	1.03548	+	2.84496i	0.116501	+	0.320083i	−0.867714	+	0.497065i	$0.834411\pi$
$80$	−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	$-0.508770\pi$
$83$	5.41059	−	1.96930i	0.593890	−	0.216158i	0.621439	+	0.783462i	$0.286548\pi$
$84$		0			0
$85$	−0.573662	+	0.481360i	−0.0622224	+	0.0522108i
$86$	3.40883	+	0.283818i	0.367584	+	0.0306049i
$87$		0			0
$88$	0.0117397	+	0.117169i	0.00125146	+	0.0124902i
$89$	−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
$92$	−8.35988	+	10.1345i	−0.871577	+	1.05660i
$93$		0			0
$94$	−8.35720	−	5.79964i	−0.861980	−	0.598187i
$95$	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	$0.109647\pi$
$98$	2.51468	+	9.22972i	0.254021	+	0.932343i
$99$		0			0
$100$	−8.46030	+	4.97974i	−0.846030	+	0.497974i
$101$	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	0.663062	−	0.748565i	$-0.269257\pi$
$103$	15.6512	−	2.75973i	1.54216	−	0.271924i	0.879098	+	0.476640i	$0.158146\pi$
$104$	12.1792	+	0.911130i	1.19426	+	0.0893436i
$105$		0			0
$106$	−1.27982	−	13.9534i	−0.124307	−	1.35528i
$107$	−1.00162			−0.0968302			−0.0484151	−	0.998827i	$-0.515417\pi$
$107$	−1.00162			−0.0968302			−0.0484151	+	0.998827i	$0.515417\pi$
$108$		0			0
$109$	7.26618			0.695973			0.347987	−	0.937499i	$-0.386865\pi$
$109$	7.26618			0.695973			0.347987	+	0.937499i	$0.386865\pi$
$110$	−0.00162649	−	0.0177331i	−0.000155080	−	0.00169079i
$111$		0			0
$112$	0.633458	−	1.83576i	0.0598561	−	0.173463i
$113$	−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
$116$	7.12665	+	12.1078i	0.661693	+	1.12418i
$117$		0			0
$118$	1.61832	+	5.93979i	0.148978	+	0.546802i
$119$	0.208739	−	1.18382i	0.0191351	−	0.108520i
$120$		0			0
$121$	10.3350	+	3.76163i	0.939545	+	0.341966i
$122$	−8.75345	−	6.07462i	−0.792500	−	0.549971i
$123$		0			0
$124$	−5.54055	−	4.57035i	−0.497556	−	0.410430i
$125$	2.59533	−	1.49841i	0.232133	−	0.134022i
$126$		0			0
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	0.801200	−	0.598397i	$-0.204195\pi$
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	−0.117627	+	0.993058i	$0.537529\pi$
$128$	9.07296	−	6.75879i	0.801944	−	0.597399i
$129$		0			0
$130$	−1.84057	−	0.153245i	−0.161428	−	0.0134405i
$131$	14.8870	−	12.4917i	1.30068	−	1.09140i	0.310657	−	0.950522i	$-0.399451\pi$
$131$	14.8870	−	12.4917i	1.30068	−	1.09140i	0.990027	−	0.140881i	$-0.0449935\pi$
$132$		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	0.465351	−	0.885126i	$-0.345928\pi$
$139$	−5.74324	−	6.84453i	−0.487135	−	0.580545i	−0.952486	+	0.304581i	$0.901484\pi$
$140$	−0.0981221	+	0.276798i	−0.00829283	+	0.0233937i
$141$		0			0
$142$	2.75702	+	3.90246i	0.231364	+	0.327487i
$143$	−0.0898857	+	0.155687i	−0.00751662	+	0.0130192i
$144$		0			0
$145$	−1.06231	−	1.83998i	−0.0882203	−	0.152802i
$146$	0.373705	−	0.810277i	0.0309280	−	0.0670590i
$147$		0			0
$148$	−8.72559	−	10.2232i	−0.717239	−	0.840340i
$149$	−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	0.149429	−	0.988772i	$-0.452257\pi$
$151$	−0.593940	−	0.104728i	−0.0483342	−	0.00852262i	−0.197763	+	0.980250i	$0.563368\pi$
$152$	−20.7417	−	5.27866i	−1.68238	−	0.428155i
$153$		0			0
$154$	0.0202972	+	0.0201275i	0.00163560	+	0.00162192i
$155$	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	$-0.191405\pi$
$158$	1.82575	+	3.87281i	0.145249	+	0.308104i
$159$		0			0
$160$	−1.38059	+	1.01054i	−0.109145	+	0.0798902i
$161$			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	$0.928285\pi$
$164$	−2.09182	+	12.4749i	−0.163344	+	0.974127i
$165$		0			0
$166$	7.36538	−	3.47225i	0.571664	−	0.269499i
$167$	−0.911752	−	5.17080i	−0.0705535	−	0.400129i	−0.999549	−	0.0300372i	$-0.990437\pi$
$167$	−0.911752	−	5.17080i	−0.0705535	−	0.400129i	0.928995	−	0.370092i	$-0.120674\pi$
$168$		0			0
$169$	4.32450	+	3.62869i	0.332654	+	0.279130i
$170$	−0.745712	+	0.752000i	−0.0571935	+	0.0576758i
$171$		0			0
$172$	4.83733	−	0.0406182i	0.368843	−	0.00309711i
$173$	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
$176$	0.0316678	+	0.163493i	0.00238705	+	0.0123237i
$177$		0			0
$178$	−13.3536	−	6.15878i	−1.00090	−	0.461620i
$179$	−5.77179	−	9.99703i	−0.431403	−	0.747213i	0.565591	−	0.824686i	$-0.308648\pi$
$179$	−5.77179	−	9.99703i	−0.431403	−	0.747213i	−0.996994	+	0.0774732i	$0.975315\pi$
$180$		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	$-0.0532510\pi$
$182$	2.42139	−	1.71067i	0.179486	−	0.126803i
$183$		0			0
$184$	−10.4642	+	15.3523i	−0.771427	+	1.13179i
$185$	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	$-0.406700\pi$
$191$	15.5567	−	5.66216i	1.12564	−	0.409699i	0.836708	+	0.547650i	$0.184477\pi$
$192$		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	$0.380396\pi$
$194$	−0.390888	+	4.69480i	−0.0280641	+	0.337067i
$195$		0			0
$196$	4.73363	+	12.6734i	0.338116	+	0.905244i
$197$	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	−0.355927	−	0.934514i	$-0.615835\pi$
$199$	3.88531	−	2.24318i	0.275422	−	0.159015i	0.631349	+	0.775499i	$0.282501\pi$
$200$	−11.2714	+	8.10580i	−0.797010	+	0.573166i
$201$		0			0
$202$	13.4648	−	19.4026i	0.947378	−	1.36516i
$203$	3.20479	+	1.16645i	0.224932	+	0.0818686i
$204$		0			0
$205$	0.332164	−	1.88379i	0.0231993	−	0.131570i
$206$	21.6852	−	5.90821i	1.51088	−	0.411644i
$207$		0			0
$208$	17.2696	−	0.290040i	1.19743	−	0.0201107i
$209$	0.202503	−	0.241333i	0.0140074	−	0.0166934i
$210$		0			0
$211$	22.1033	−	3.89740i	1.52165	−	0.268308i	0.650570	−	0.759446i	$-0.274530\pi$
$211$	22.1033	−	3.89740i	1.52165	−	0.268308i	0.871082	+	0.491138i	$0.163419\pi$
$212$	−3.60475	−	19.4854i	−0.247575	−	1.33826i
$213$		0			0
$214$	−1.41058	+	0.129380i	−0.0964254	+	0.00884421i
$215$	−0.731549			−0.0498912
$216$		0			0
$217$	−1.74349			−0.118356
$218$	10.2330	−	0.938575i	0.693064	−	0.0635683i
$219$		0			0
$220$	−0.00458119	−	0.0247635i	−0.000308864	−	0.00166955i
$221$	10.5289	−	1.85654i	0.708253	−	0.124884i
$222$		0			0
$223$	−11.7737	+	14.0314i	−0.788428	+	0.939612i	−0.999281	−	0.0379061i	$-0.987931\pi$
$223$	−11.7737	+	14.0314i	−0.788428	+	0.939612i	0.210854	+	0.977518i	$0.432376\pi$
$224$	0.654974	−	2.66712i	0.0437623	−	0.178205i
$225$		0			0
$226$	−19.7426	+	5.37896i	−1.31326	+	0.357803i
$227$	−3.40406	+	19.3054i	−0.225936	+	1.28134i	0.634953	+	0.772551i	$0.281020\pi$
$227$	−3.40406	+	19.3054i	−0.225936	+	1.28134i	−0.860888	+	0.508794i	$0.830092\pi$
$228$		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	$0.671078\pi$
$230$	1.60188	−	2.30828i	0.105625	−	0.152204i
$231$		0			0
$232$	11.6004	+	16.1309i	0.761606	+	1.05904i
$233$	−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
$236$	3.04633	+	8.15597i	0.198299	+	0.530909i
$237$		0			0
$238$	0.141053	−	1.69414i	0.00914313	−	0.109814i
$239$	−4.95760	+	4.15992i	−0.320680	+	0.269083i	−0.788890	−	0.614535i	$-0.789344\pi$
$239$	−4.95760	+	4.15992i	−0.320680	+	0.269083i	0.468209	+	0.883618i	$0.344899\pi$
$240$		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
$248$	−8.39312	−	5.72076i	−0.532964	−	0.363269i
$249$		0			0
$250$	3.46146	−	2.44546i	0.218922	−	0.154664i
$251$	1.09113	−	1.88989i	0.0688715	−	0.119289i	−0.829533	−	0.558457i	$-0.811393\pi$
$251$	1.09113	−	1.88989i	0.0688715	−	0.119289i	0.898405	+	0.439168i	$0.144727\pi$
$252$		0			0
$253$	−0.136739	−	0.236839i	−0.00859670	−	0.0148899i
$254$	11.4233	+	5.26851i	0.716763	+	0.330576i
$255$		0			0
$256$	11.9044	−	10.6904i	0.744027	−	0.668149i
$257$	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
$260$	−2.61187	+	0.0219314i	−0.161981	+	0.00136013i
$261$		0			0
$262$	19.3518	−	19.5150i	1.19556	−	1.20564i
$263$	7.84733	+	6.58469i	0.483887	+	0.406029i	0.851829	−	0.523819i	$-0.175493\pi$
$263$	7.84733	+	6.58469i	0.483887	+	0.406029i	−0.367943	+	0.929849i	$0.619938\pi$
$264$		0			0
$265$	0.520366	+	2.95114i	0.0319658	+	0.181287i
$266$	−4.69945	+	2.21546i	−0.288142	+	0.135838i
$267$		0			0
$268$	−3.68407	+	21.9706i	−0.225041	+	1.34207i
$269$			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	$0.0322642\pi$
$271$			3.33151i			0.202375i	−0.994867	+	0.101188i	$0.967736\pi$
$272$	6.23785	−	7.69271i	0.378225	−	0.466439i
$273$		0			0
$274$	9.24909	+	19.6193i	0.558758	+	1.18524i
$275$	−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	$0.682188\pi$
$278$	−8.97233	−	8.89730i	−0.538124	−	0.533625i
$279$		0			0
$280$	−0.102431	+	0.402489i	−0.00612145	+	0.0240533i
$281$	−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	$0.262422\pi$
$283$	−5.26641	+	14.4693i	−0.313055	+	0.860113i	−0.992036	+	0.125956i	$0.959800\pi$
$284$	4.38680	+	5.13971i	0.260309	+	0.304986i
$285$		0			0
$286$	−0.106476	+	0.230864i	−0.00629606	+	0.0136513i
$287$	1.53526	+	2.65916i	0.0906238	+	0.156965i
$288$		0			0
$289$	−5.43473	+	9.41323i	−0.319690	+	0.553720i
$290$	−1.73373	−	2.45403i	−0.101808	−	0.144106i
$291$		0			0
$292$	0.421625	−	1.18939i	0.0246738	−	0.0696036i
$293$	−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
$302$	−0.849975	−	0.0707687i	−0.0489106	−	0.00407228i
$303$		0			0
$304$	−29.8924	−	4.75473i	−1.71445	−	0.272702i
$305$	1.97339	+	1.13934i	0.112996	+	0.0652382i
$306$		0			0
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.912136	−	0.409887i	$-0.865568\pi$
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.101096	+	0.994877i	$0.532235\pi$
$308$	0.0311845	+	0.0257238i	0.00177690	+	0.00146575i
$309$		0			0
$310$	1.26194	+	0.875747i	0.0716733	+	0.0497391i
$311$	−18.8205	−	6.85012i	−1.06722	−	0.388435i	−0.252081	−	0.967706i	$-0.581115\pi$
$311$	−18.8205	−	6.85012i	−1.06722	−	0.388435i	−0.815135	+	0.579272i	$0.803337\pi$
$312$		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	$0.889412\pi$
$314$	−3.85640	−	14.1543i	−0.217629	−	0.798774i
$315$		0			0
$316$	3.07146	+	5.21825i	0.172783	+	0.293549i
$317$	−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
$320$	−1.81376	+	1.60148i	−0.101392	+	0.0895253i
$321$		0			0
$322$	0.411939	+	4.49123i	0.0229565	+	0.250287i
$323$	−18.7360			−1.04250
$324$		0			0
$325$	−21.1951			−1.17569
$326$	0.736827	+	8.03337i	0.0408090	+	0.444927i
$327$		0			0
$328$	−1.33452	+	17.8387i	−0.0736866	+	0.984975i
$329$	−3.43911	+	0.606408i	−0.189604	+	0.0334323i
$330$		0			0
$331$	12.9390	−	15.4201i	0.711190	−	0.847563i	−0.282554	−	0.959252i	$-0.591181\pi$
$331$	12.9390	−	15.4201i	0.711190	−	0.847563i	0.993743	+	0.111689i	$0.0356259\pi$
$332$	9.92416	−	5.84137i	0.544659	−	0.320587i
$333$		0			0
$334$	−1.95194	−	7.16428i	−0.106805	−	0.392012i
$335$	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	$0.728254\pi$
$338$	6.55893	+	4.55169i	0.356759	+	0.247579i
$339$		0			0
$340$	−0.953052	+	1.15537i	−0.0516865	+	0.0626586i
$341$	0.129480	−	0.0747552i	0.00701173	−	0.00404822i
$342$		0			0
$343$	5.78720	+	3.34124i	0.312480	+	0.180410i
$344$	6.80717	−	0.682042i	0.367018	−	0.0367733i
$345$		0			0
$346$	1.95510	+	0.162781i	0.105107	+	0.00875117i
$347$	−13.6769	+	11.4763i	−0.734213	+	0.616078i	−0.931277	−	0.364313i	$-0.881304\pi$
$347$	−13.6769	+	11.4763i	−0.734213	+	0.616078i	0.197064	+	0.980391i	$0.436859\pi$
$348$		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
$356$	−19.6015	−	6.94853i	−1.03888	−	0.368271i
$357$		0			0
$358$	−9.41974	−	13.3333i	−0.497849	−	0.704686i
$359$	−9.46695	+	16.3972i	−0.499647	+	0.865413i	−1.00000		0.000407927i	$-0.999870\pi$
$359$	−9.46695	+	16.3972i	−0.499647	+	0.865413i	0.500353	+	0.865821i	$0.333203\pi$
$360$		0			0
$361$	19.1302	+	33.1344i	1.00685	+	1.74392i
$362$	10.1553	−	22.0190i	0.533752	−	1.15729i
$363$		0			0
$364$	3.18908	−	2.72191i	0.167153	−	0.142667i
$365$	−0.0652682	+	0.179323i	−0.00341629	+	0.00938619i
$366$		0			0
$367$	−23.4580	−	4.13627i	−1.22450	−	0.215912i	−0.476236	−	0.879317i	$-0.657999\pi$
$367$	−23.4580	−	4.13627i	−1.22450	−	0.215912i	−0.748260	+	0.663406i	$0.769110\pi$
$368$	−12.7536	+	22.9724i	−0.664828	+	1.19752i
$369$		0			0
$370$	2.04106	+	2.02400i	0.106110	+	0.105223i
$371$	−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	$-0.245193\pi$
$374$	0.0621638	+	0.131863i	0.00321442	+	0.00681845i
$375$		0			0
$376$	−18.5456	−	8.36521i	−0.956415	−	0.431403i
$377$			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	$-0.332662\pi$
$380$	4.51428	+	0.756963i	0.231578	+	0.0388314i
$381$		0			0
$382$	21.1771	−	9.98349i	1.08351	−	0.510800i
$383$	−0.261068	−	1.48059i	−0.0133400	−	0.0756548i	0.977411	−	0.211347i	$-0.0677851\pi$
$383$	−0.261068	−	1.48059i	−0.0133400	−	0.0756548i	−0.990751	+	0.135693i	$0.956674\pi$
$384$		0			0
$385$	−0.00468303	−	0.00392953i	−0.000238670	−	0.000200268i
$386$	−8.76604	+	8.83996i	−0.446180	+	0.449942i
$387$		0			0
$388$	0.0559413	+	6.66219i	0.00283999	+	0.338222i
$389$	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
$392$	8.30341	+	17.2366i	0.419386	+	0.870578i
$393$		0			0
$394$	16.0495	+	7.40214i	0.808563	+	0.372914i
$395$	−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	$0.330424\pi$
$398$	5.18193	−	3.66095i	0.259747	−	0.183507i
$399$		0			0
$400$	−14.8265	+	12.8713i	−0.741327	+	0.643567i
$401$	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	$0.365429\pi$
$410$	0.224456	−	2.69586i	0.0110851	−	0.133139i
$411$		0			0
$412$	29.7761	−	11.1216i	1.46696	−	0.547923i
$413$	1.83029	+	1.05672i	0.0900626	+	0.0519976i
$414$		0			0
$415$	−1.50814	+	0.870727i	−0.0740319	+	0.0427423i
$416$	24.2834	−	2.63919i	1.19059	−	0.129397i
$417$		0			0
$418$	0.254012	−	0.366028i	0.0124241	−	0.0179030i
$419$	22.7569	+	8.28284i	1.11175	+	0.404643i	0.831635	−	0.555323i	$-0.187405\pi$
$419$	22.7569	+	8.28284i	1.11175	+	0.404643i	0.280114	+	0.959967i	$0.409628\pi$
$420$		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	$-0.295278\pi$
$422$	30.6247	−	8.34381i	1.49078	−	0.406170i
$423$		0			0
$424$	−7.59351	−	26.9756i	−0.368773	−	1.31005i
$425$	−7.81210	+	9.31010i	−0.378942	+	0.451606i
$426$		0			0
$427$	−3.60217	+	0.635160i	−0.174321	+	0.0307375i
$428$	−1.96981	+	0.364411i	−0.0952146	+	0.0176145i
$429$		0			0
$430$	−1.03024	+	0.0944945i	−0.0496827	+	0.00455693i
$431$	38.5608			1.85741			0.928705	−	0.370820i	$-0.120923\pi$
$431$	38.5608			1.85741			0.928705	+	0.370820i	$0.120923\pi$
$432$		0			0
$433$	−6.56251			−0.315374			−0.157687	−	0.987489i	$-0.550404\pi$
$433$	−6.56251			−0.315374			−0.157687	+	0.987489i	$0.550404\pi$
$434$	−2.45536	+	0.225207i	−0.117861	+	0.0108103i
$435$		0			0
$436$	14.2899	−	2.64360i	0.684361	−	0.126605i
$437$	48.9513	−	8.63143i	2.34166	−	0.412897i
$438$		0			0
$439$	−1.17279	+	1.39768i	−0.0559744	+	0.0667077i	−0.793305	−	0.608824i	$-0.791641\pi$
$439$	−1.17279	+	1.39768i	−0.0559744	+	0.0667077i	0.737331	+	0.675532i	$0.236086\pi$
$440$	−0.00965041	−	0.0342827i	−0.000460065	−	0.00163437i
$441$		0			0
$442$	14.5881	−	3.97459i	0.693886	−	0.189052i
$443$	0.302973	−	1.71824i	0.0143947	−	0.0816362i	−0.976764	−	0.214317i	$-0.931247\pi$
$443$	0.302973	−	1.71824i	0.0143947	−	0.0816362i	0.991159	+	0.132681i	$0.0423585\pi$
$444$		0			0
$445$	2.95530	+	1.07564i	0.140095	+	0.0509903i
$446$	−14.7685	+	21.2813i	−0.699310	+	1.00770i
$447$		0			0
$448$	0.577888	−	3.84072i	0.0273026	−	0.181457i
$449$	−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
$452$	−27.1088	+	10.1254i	−1.27509	+	0.476258i
$453$		0			0
$454$	−2.30026	+	27.6275i	−0.107957	+	1.29663i
$455$	−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	0.603618	−	0.797274i	$-0.293725\pi$
$463$	−6.16175	−	7.34328i	−0.286361	−	0.341271i	−0.889979	+	0.456002i	$0.849281\pi$
$464$	18.4206	+	21.2187i	0.855153	+	0.985053i
$465$		0			0
$466$	−8.67587	+	6.12935i	−0.401902	+	0.283937i
$467$	8.74737	−	15.1509i	0.404780	−	0.701099i	−0.589516	−	0.807757i	$-0.700681\pi$
$467$	8.74737	−	15.1509i	0.404780	−	0.701099i	0.994296	+	0.106657i	$0.0340148\pi$
$468$		0			0
$469$	2.70388	+	4.68326i	0.124854	+	0.216253i
$470$	2.79383	+	1.28853i	0.128870	+	0.0594355i
$471$		0			0
$472$	5.34366	+	11.0926i	0.245962	+	0.510577i
$473$	−0.0344412	+	0.0946266i	−0.00158361	+	0.00435093i
$474$		0			0
$475$	36.5788	+	6.44983i	1.67835	+	0.295938i
$476$	−0.0201866	−	2.40407i	−0.000925251	−	0.110191i
$477$		0			0
$478$	−6.44446	+	6.49880i	−0.294763	+	0.297248i
$479$	−20.0678	−	16.8388i	−0.916919	−	0.769386i	0.0565037	−	0.998402i	$-0.482005\pi$
$479$	−20.0678	−	16.8388i	−0.916919	−	0.769386i	−0.973423	+	0.229016i	$0.926449\pi$
$480$		0			0
$481$	−5.03898	−	28.5775i	−0.229758	−	1.30302i
$482$	0.887657	−	0.418467i	0.0404317	−	0.0190607i
$483$		0			0
$484$	21.6937	+	3.63763i	0.986076	+	0.165347i
$485$		−	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	$0.948501\pi$
$488$	−19.4249	−	8.76184i	−0.879323	−	0.396630i
$489$		0			0
$490$	−1.23375	−	2.61705i	−0.0557352	−	0.118226i
$491$	−3.43007	−	19.4529i	−0.154797	−	0.877897i	−0.958971	−	0.283503i	$-0.908503\pi$
$491$	−3.43007	−	19.4529i	−0.154797	−	0.877897i	0.804174	−	0.594393i	$-0.202608\pi$
$492$		0			0
$493$	13.3239	+	11.1801i	0.600081	+	0.503527i
$494$	−32.8115	−	32.5372i	−1.47626	−	1.46392i
$495$		0			0
$496$	−12.5590	−	6.97241i	−0.563916	−	0.313071i
$497$	1.61539	+	0.284836i	0.0724600	+	0.0127767i
$498$		0			0
$499$	−13.5189	+	37.1430i	−0.605191	+	1.66275i	0.135400	+	0.990791i	$0.456768\pi$
$499$	−13.5189	+	37.1430i	−0.605191	+	1.66275i	−0.740591	+	0.671956i	$0.765454\pi$
$500$	4.55890	−	3.89106i	0.203880	−	0.174014i
$501$		0			0
$502$	1.29252	−	2.80248i	0.0576881	−	0.125081i
$503$	19.5426	+	33.8489i	0.871364	+	1.50925i	0.860587	+	0.509304i	$0.170097\pi$
$503$	19.5426	+	33.8489i	0.871364	+	1.50925i	0.0107769	+	0.999942i	$0.496570\pi$
$504$		0			0
$505$	−2.52541	+	4.37413i	−0.112379	+	0.194646i
$506$	−0.223162	−	0.315878i	−0.00992077	−	0.0140425i
$507$		0			0
$508$	16.7680	+	5.94410i	0.743961	+	0.263727i
$509$	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
$518$	−4.59819	−	0.382844i	−0.202033	−	0.0168212i
$519$		0			0
$520$	−3.67547	+	0.368262i	−0.161180	+	0.0161494i
$521$	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	−0.341505	−	0.939880i	$-0.610937\pi$
$523$	6.89969	−	3.98354i	0.301702	−	0.174188i	0.643207	+	0.765692i	$0.277603\pi$
$524$	24.7325	−	29.9827i	1.08044	−	1.30980i
$525$		0			0
$526$	11.9020	+	8.25959i	0.518950	+	0.360135i
$527$	−8.35546	−	3.04114i	−0.363969	−	0.132474i
$528$		0			0
$529$	3.49884	−	19.8429i	0.152124	−	0.862736i
$530$	1.11403	+	4.08888i	0.0483905	+	0.177610i
$531$		0			0
$532$	−6.33207	+	3.72706i	−0.274530	+	0.161589i
$533$	−17.5542	+	20.9203i	−0.760356	+	0.906157i
$534$		0			0
$535$	0.298337	−	0.0526049i	0.0128982	−	0.00227431i
$536$	−2.35033	+	31.4171i	−0.101519	+	1.35701i
$537$		0			0
$538$	0.407173	+	4.43928i	0.0175545	+	0.191391i
$539$	−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	$0.442120\pi$
$542$	0.430333	+	4.69178i	0.0184844	+	0.201529i
$543$		0			0
$544$	7.79110	−	11.6394i	0.334041	−	0.499036i
$545$	−2.16426	+	0.381618i	−0.0927069	+	0.0163467i
$546$		0			0
$547$	11.2369	−	13.3916i	0.480453	−	0.572582i	−0.470309	−	0.882502i	$-0.655858\pi$
$547$	11.2369	−	13.3916i	0.480453	−	0.572582i	0.950763	+	0.309920i	$0.100302\pi$
$548$	15.5597	+	26.4351i	0.664679	+	1.12925i
$549$		0			0
$550$	−0.0759708	−	0.278839i	−0.00323941	−	0.0118897i
$551$	9.23054	−	52.3490i	0.393234	−	2.23014i
$552$		0			0
$553$	1.38121	+	0.502719i	0.0587350	+	0.0213778i
$554$	4.85129	+	3.36664i	0.206111	+	0.143035i
$555$		0			0
$556$	−13.7850	−	11.3711i	−0.584615	−	0.482243i
$557$	−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
$560$	−0.0922646	+	0.580058i	−0.00389889	+	0.0245119i
$561$		0			0
$562$	−27.6621	−	2.30314i	−1.16685	−	0.0971520i
$563$	4.79979	−	4.02750i	0.202287	−	0.169739i	−0.536017	−	0.844207i	$-0.680072\pi$
$563$	4.79979	−	4.02750i	0.202287	−	0.169739i	0.738304	+	0.674468i	$0.235627\pi$
$564$		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	0.999979	−	0.00640314i	$-0.00203820\pi$
$571$	19.5951	+	23.3525i	0.820029	+	0.977273i	−0.179950	+	0.983676i	$0.557594\pi$
$572$	−0.120130	+	0.338880i	−0.00502287	+	0.0141693i
$573$		0			0
$574$	2.50560	+	3.54658i	0.104582	+	0.148032i
$575$	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	$0.965286\pi$
$578$	−6.43783	+	13.9587i	−0.267779	+	0.580605i
$579$		0			0
$580$	−2.75860	−	3.23207i	−0.114545	−	0.134204i
$581$	0.956081	−	2.62681i	0.0396649	−	0.108979i
$582$		0			0
$583$	0.406232	+	0.0716296i	0.0168244	+	0.00296659i
$584$	0.440143	−	1.72948i	0.0182132	−	0.0715662i
$585$		0			0
$586$	−18.6999	−	18.5436i	−0.772486	−	0.766027i
$587$	33.1376	+	27.8057i	1.36773	+	1.14767i	0.973508	+	0.228653i	$0.0734320\pi$
$587$	33.1376	+	27.8057i	1.36773	+	1.14767i	0.394227	+	0.919013i	$0.371012\pi$
$588$		0			0
$589$	4.71881	+	26.7617i	0.194435	+	1.10270i
$590$	−0.793980	−	1.68420i	−0.0326876	−	0.0693374i
$591$		0			0
$592$	−20.8794	−	16.9306i	−0.858139	−	0.695845i
$593$		−	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
$596$	−0.569525	+	3.39646i	−0.0233286	+	0.139124i
$597$		0			0
$598$	−36.2832	+	17.1049i	−1.48373	+	0.699473i
$599$	6.52625	+	37.0122i	0.266655	+	1.51228i	0.764279	+	0.644885i	$0.223095\pi$
$599$	6.52625	+	37.0122i	0.266655	+	1.51228i	−0.497624	+	0.867393i	$0.665794\pi$
$600$		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	$0.656930\pi$
$602$	1.16935	−	1.17921i	0.0476591	−	0.0480609i
$603$		0			0
$604$	−1.20616	+	0.0101279i	−0.0490781	+	0.000412100i
$605$	−3.27588	−	0.577627i	−0.133184	−	0.0234839i
$606$		0			0
$607$	9.92909	−	27.2799i	0.403009	−	1.10726i	−0.557783	−	0.829987i	$-0.688348\pi$
$607$	9.92909	−	27.2799i	0.403009	−	1.10726i	0.960792	−	0.277271i	$-0.0894301\pi$
$608$	−42.7118	−	2.83487i	−1.73219	−	0.114969i
$609$		0			0
$610$	2.92629	+	1.34963i	0.118482	+	0.0546447i
$611$	−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	$0.308156\pi$
$614$	−23.6780	+	16.7281i	−0.955566	+	0.675091i
$615$		0			0
$616$	0.0472399	+	0.0321987i	0.00190335	+	0.00129732i
$617$	−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	0.996990	−	0.0775360i	$-0.0247053\pi$
$619$	4.56324	+	12.5374i	0.183412	+	0.503921i	−0.813577	+	0.581457i	$0.802483\pi$
$620$	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
$626$	−2.07006	+	24.8627i	−0.0827364	+	0.993714i
$627$		0			0
$628$	−7.25929	−	19.4354i	−0.289677	−	0.775557i
$629$	−14.4101	−	8.31969i	−0.574570	−	0.331728i
$630$		0			0
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.335117	−	0.942176i	$-0.391224\pi$
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.983507	+	0.180868i	$0.0578908\pi$
$632$	4.99959	+	6.95213i	0.198873	+	0.276541i
$633$		0			0
$634$	−3.46441	+	4.99216i	−0.137589	+	0.198264i
$635$	−2.52810	−	0.920154i	−0.100325	−	0.0365152i
$636$		0			0
$637$	−5.07197	+	28.7646i	−0.200959	+	1.13969i
$638$	−0.399055	+	0.108724i	−0.0157987	+	0.00430443i
$639$		0			0
$640$	−2.34745	+	2.48965i	−0.0927913	+	0.0984120i
$641$	−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	−0.161265	−	0.986911i	$-0.551557\pi$
$643$	0.627325	−	0.110614i	0.0247393	−	0.00436221i	0.186004	+	0.982549i	$0.440446\pi$
$644$	1.16027	+	6.27180i	0.0457210	+	0.247144i
$645$		0			0
$646$	−26.3859	+	2.42013i	−1.03814	+	0.0952189i
$647$	7.26586			0.285650			0.142825	−	0.989748i	$-0.454381\pi$
$647$	7.26586			0.285650			0.142825	+	0.989748i	$0.454381\pi$
$648$		0			0
$649$	−0.181235			−0.00711408
$650$	−29.8491	+	2.73778i	−1.17078	+	0.107384i
$651$		0			0
$652$	2.07535	+	11.2182i	0.0812769	+	0.439340i
$653$	−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
$656$	0.424819	+	25.2946i	0.0165864	+	0.987588i
$657$		0			0
$658$	−4.76497	+	1.29824i	−0.185758	+	0.0506105i
$659$	−2.56367	+	14.5393i	−0.0998663	+	0.566370i	0.893281	+	0.449499i	$0.148397\pi$
$659$	−2.56367	+	14.5393i	−0.0998663	+	0.566370i	−0.993147	+	0.116871i	$0.962714\pi$
$660$		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	$0.738539\pi$
$662$	16.2302	−	23.3874i	0.630803	−	0.908978i
$663$		0			0
$664$	13.2217	−	9.50832i	0.513101	−	0.368994i
$665$	0.962265	−	0.555564i	0.0373150	−	0.0215438i
$666$		0			0
$667$	−39.9619	−	23.0720i	−1.54733	−	0.893352i
$668$	−3.67433	−	9.83734i	−0.142164	−	0.380618i
$669$		0			0
$670$	0.395308	−	4.74789i	0.0152721	−	0.183427i
$671$	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
$680$	−1.19295	+	1.75021i	−0.0457474	+	0.0671176i
$681$		0			0
$682$	0.172691	−	0.122003i	0.00661267	−	0.00467173i
$683$	−12.3153	+	21.3308i	−0.471233	+	0.816200i	−0.999459	−	0.0329044i	$-0.989524\pi$
$683$	−12.3153	+	21.3308i	−0.471233	+	0.816200i	0.528225	+	0.849104i	$0.322858\pi$
$684$		0			0
$685$	−2.31937	−	4.01726i	−0.0886185	−	0.153492i
$686$	8.58172	+	3.95794i	0.327652	+	0.151115i
$687$		0			0
$688$	9.49845	−	1.83981i	0.362125	−	0.0701420i
$689$	14.6326	−	40.2027i	0.557458	−	1.53160i
$690$		0			0
$691$	14.4784	+	2.55293i	0.550784	+	0.0971181i	0.442113	−	0.896960i	$-0.354229\pi$
$691$	14.4784	+	2.55293i	0.550784	+	0.0971181i	0.108672	+	0.994078i	$0.465340\pi$
$692$	2.77440	−	0.0232961i	0.105467	−	0.000885586i
$693$		0			0
$694$	−17.7788	+	17.9287i	−0.674873	+	0.680564i
$695$	2.07012	+	1.73704i	0.0785243	+	0.0658897i
$696$		0			0
$697$	2.71925	+	15.4216i	0.102999	+	0.584135i
$698$	16.7222	−	7.88334i	0.632945	−	0.298389i
$699$		0			0
$700$	−0.788188	+	4.70050i	−0.0297907	+	0.177662i
$701$			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
$704$	0.121761	+	0.310008i	0.00458905	+	0.0116839i
$705$		0			0
$706$	−12.9578	−	27.4862i	−0.487672	−	1.03446i
$707$	−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	$0.986080\pi$
$710$	−1.02615	−	1.01757i	−0.0385106	−	0.0381886i
$711$		0			0
$712$	−28.5024	−	7.25370i	−1.06817	−	0.271844i
$713$	23.2312	+	4.09629i	0.870016	+	0.153407i
$714$		0			0
$715$	0.0185962	−	0.0510927i	0.000695460	−	0.00191076i
$716$	−14.9881	−	17.5605i	−0.560132	−	0.656268i
$717$		0			0
$718$	−11.2143	+	24.3151i	−0.418514	+	0.907432i
$719$	0.482259	+	0.835298i	0.0179852	+	0.0311514i	0.874878	−	0.484343i	$-0.160941\pi$
$719$	0.482259	+	0.835298i	0.0179852	+	0.0311514i	−0.856893	+	0.515495i	$0.827608\pi$
$720$		0			0
$721$	3.85790	−	6.68207i	0.143676	−	0.248853i
$722$	31.2211	+	44.1922i	1.16193	+	1.64467i
$723$		0			0
$724$	11.4575	−	32.3212i	0.425816	−	1.20121i
$725$	−22.1640	−	26.4140i	−0.823151	−	0.980993i
$726$		0			0
$727$	7.16819	+	19.6944i	0.265854	+	0.730427i	0.998745	+	0.0500812i	$0.0159480\pi$
$727$	7.16819	+	19.6944i	0.265854	+	0.730427i	−0.732892	+	0.680345i	$0.761830\pi$
$728$	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	$0.267224\pi$
$734$	−33.5702	−	2.79505i	−1.23910	−	0.103167i
$735$		0			0
$736$	−14.9936	+	33.9994i	−0.552671	+	1.25324i
$737$	−0.401606	−	0.231867i	−0.0147934	−	0.00854095i
$738$		0			0
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	−0.781017	−	0.624510i	$-0.785299\pi$
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	0.150333	+	0.988635i	$0.451965\pi$
$740$	3.13588	+	2.58675i	0.115277	+	0.0950910i
$741$		0			0
$742$	−5.58882	−	3.87847i	−0.205172	−	0.142383i
$743$	−36.3877	−	13.2440i	−1.33494	−	0.485877i	−0.426721	−	0.904383i	$-0.640331\pi$
$743$	−36.3877	−	13.2440i	−1.33494	−	0.485877i	−0.908214	+	0.418507i	$0.862554\pi$
$744$		0			0
$745$	0.0904359	−	0.512888i	0.00331332	−	0.0187907i
$746$	−8.05778	−	29.5748i	−0.295016	−	1.08281i
$747$		0			0
$748$	0.104578	+	0.177673i	0.00382376	+	0.00649635i
$749$	−0.312575	+	0.372512i	−0.0114212	+	0.0136113i
$750$		0			0
$751$	22.7048	−	4.00346i	0.828508	−	0.146088i	0.256716	−	0.966487i	$-0.417359\pi$
$751$	22.7048	−	4.00346i	0.828508	−	0.146088i	0.571792	+	0.820398i	$0.306248\pi$
$752$	−27.1983	−	9.38521i	−0.991820	−	0.342243i
$753$		0			0
$754$	3.91811	+	42.7179i	0.142689	+	1.55569i
$755$	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	$0.293061\pi$
$758$	−4.35024	−	47.4292i	−0.158008	−	1.72271i
$759$		0			0
$760$	6.45525	+	0.482921i	0.234156	+	0.0175174i
$761$	−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
$764$	28.5342	−	16.7952i	1.03233	−	0.607630i
$765$		0			0
$766$	−0.558912	−	2.05140i	−0.0201943	−	0.0741201i
$767$	−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	$0.481040\pi$
$770$	−0.00710271	−	0.00492906i	−0.000255964	−	0.000177631i
$771$		0			0
$772$	−11.2034	+	13.5816i	−0.403218	+	0.488814i
$773$	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
$776$	0.939341	+	9.37516i	0.0337204	+	0.336549i
$777$		0			0
$778$	5.44238	+	0.453131i	0.195119	+	0.0162455i
$779$	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	$-0.203029\pi$
$787$	2.17335	+	2.59010i	0.0774716	+	0.0923271i	−0.725916	+	0.687783i	$0.758584\pi$
$788$	23.5587	+	8.35133i	0.839244	+	0.297504i
$789$		0			0
$790$	−0.747208	−	1.05764i	−0.0265845	−	0.0376293i
$791$	−3.51231	+	6.08351i	−0.124884	+	0.216305i
$792$		0			0
$793$	−16.2661	−	28.1737i	−0.577625	−	1.00048i
$794$	−11.6139	+	25.1816i	−0.412162	+	0.893661i
$795$		0			0
$796$	6.82484	−	5.82507i	0.241900	−	0.206464i
$797$	−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
$800$	−19.2177	+	20.0419i	−0.679447	+	0.708588i
$801$		0			0
$802$	21.7835	+	21.6013i	0.769201	+	0.762769i
$803$	0.0201228	+	0.0168850i	0.000710117	+	0.000595859i
$804$		0			0
$805$	−0.167491	−	0.949891i	−0.00590330	−	0.0334793i
$806$	−9.35128	−	19.8360i	−0.329385	−	0.698695i
$807$		0			0
$808$	19.4212	−	43.0564i	0.683234	−	1.51472i
$809$		−	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	$0.0776791\pi$
$811$			13.7618i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$812$	6.72702	+	1.12800i	0.236072	+	0.0395850i
$813$		0			0
$814$	0.357899	−	0.168724i	0.0125444	−	0.00591377i
$815$	−0.299589	−	1.69905i	−0.0104941	−	0.0595152i
$816$		0			0
$817$	−14.0208	−	11.7648i	−0.490524	−	0.411599i
$818$	−10.9513	+	11.0436i	−0.382903	+	0.386131i
$819$		0			0
$820$	−0.0321227	−	3.82557i	−0.00112177	−	0.133595i
$821$	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	$-0.609712\pi$
$823$	15.0879	−	41.4538i	0.525932	−	1.44499i	0.863820	−	0.503801i	$-0.168065\pi$
$824$	40.4972	−	19.5088i	1.41079	−	0.679621i
$825$		0			0
$826$	2.71409	+	1.25176i	0.0944354	+	0.0435542i
$827$	−5.67028	−	9.82121i	−0.197175	−	0.341517i	0.750436	−	0.660943i	$-0.229843\pi$
$827$	−5.67028	−	9.82121i	−0.197175	−	0.341517i	−0.947611	+	0.319426i	$0.896510\pi$
$828$		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	$-0.00174758\pi$
$830$	−2.01145	+	1.42105i	−0.0698184	+	0.0493255i
$831$		0			0
$832$	33.8574	−	6.85347i	1.17380	−	0.237601i
$833$	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	$-0.545996\pi$
$839$	11.0585	−	4.02496i	0.381781	−	0.138957i	0.525779	+	0.850621i	$0.323774\pi$
$840$		0			0
$841$	−15.5866	+	13.0787i	−0.537469	+	0.450990i
$842$	4.29615	−	51.5994i	0.148055	−	1.77823i
$843$		0			0
$844$	42.0510	−	15.7064i	1.44745	−	0.540637i
$845$	−1.47865	−	0.853700i	−0.0508672	−	0.0293682i
$846$		0			0
$847$	4.62422	−	2.66980i	0.158890	−	0.0917353i
$848$	−14.1784	−	37.0090i	−0.486888	−	1.27089i
$849$		0			0
$850$	−9.79920	+	14.1205i	−0.336110	+	0.484330i
$851$	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	$0.786297\pi$
$854$	−4.99090	+	1.35979i	−0.170785	+	0.0465311i
$855$		0			0
$856$	−2.72702	+	0.767643i	−0.0932077	+	0.0262375i
$857$	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	−0.783675	−	0.621171i	$-0.786657\pi$
$859$	−38.3251	+	6.75775i	−1.30764	+	0.230571i	−0.523961	+	0.851743i	$0.675546\pi$
$860$	−1.43869	+	0.266154i	−0.0490588	+	0.00907577i
$861$		0			0
$862$	54.3053	−	4.98092i	1.84965	−	0.169651i
$863$	−48.5663			−1.65322			−0.826608	−	0.562778i	$-0.809732\pi$
$863$	−48.5663			−1.65322			−0.826608	+	0.562778i	$0.809732\pi$
$864$		0			0
$865$	−0.419573			−0.0142659
$866$	−9.24200	+	0.847683i	−0.314056	+	0.0288054i
$867$		0			0
$868$	−3.42880	+	0.634320i	−0.116381	+	0.0215302i
$869$	−0.124130	+	0.0218875i	−0.00421083	+	0.000742483i
$870$		0			0
$871$	−30.9161	+	36.8444i	−1.04755	+	1.24842i
$872$	19.7830	−	5.56881i	0.669937	−	0.188584i
$873$		0			0
$874$	67.8233	−	18.4787i	2.29416	−	0.625052i
$875$	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	$0.518343\pi$
$878$	−1.47111	+	2.11985i	−0.0496475	+	0.0715414i
$879$		0			0
$880$	−0.0180190	−	0.0470339i	−0.000607421	−	0.00158551i
$881$	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	0.184154	−	0.982897i	$-0.441046\pi$
$883$	−17.0858	−	9.86450i	−0.574984	−	0.331967i	−0.759137	+	0.650931i	$0.774379\pi$
$884$	20.0311	−	7.48178i	0.673718	−	0.251640i
$885$		0			0
$886$	0.204731	−	2.45894i	0.00687807	−	0.0826098i
$887$	−35.6487	+	29.9128i	−1.19697	+	1.00437i	−0.197254	+	0.980352i	$0.563202\pi$
$887$	−35.6487	+	29.9128i	−1.19697	+	1.00437i	−0.999711	+	0.0240206i	$0.992353\pi$
$888$		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
$896$	0.317733	−	5.48354i	0.0106147	−	0.183192i
$897$		0			0
$898$	−10.6719	+	7.53952i	−0.356126	+	0.251597i
$899$	12.6135	−	21.8472i	0.420683	−	0.728645i
$900$		0			0
$901$	−12.2661	−	21.2454i	−0.408642	−	0.707788i
$902$	−0.338144	−	0.155954i	−0.0112590	−	0.00519271i
$903$		0			0
$904$	−36.8695	+	17.7612i	−1.22626	+	0.590730i
$905$	−1.77364	+	4.87305i	−0.0589579	+	0.161986i
$906$		0			0
$907$	−34.2556	−	6.04019i	−1.13744	−	0.200561i	−0.426954	−	0.904273i	$-0.640413\pi$
$907$	−34.2556	−	6.04019i	−1.13744	−	0.200561i	−0.710485	+	0.703712i	$0.751524\pi$
$908$	0.329198	+	39.2051i	0.0109248	+	1.30107i
$909$		0			0
$910$	−0.631379	+	0.636702i	−0.0209300	+	0.0211065i
$911$	22.9255	+	19.2368i	0.759557	+	0.637344i	0.938012	−	0.346604i	$-0.112665\pi$
$911$	22.9255	+	19.2368i	0.759557	+	0.637344i	−0.178454	+	0.983948i	$0.557110\pi$
$912$		0			0
$913$	0.0416261	+	0.236073i	0.00137762	+	0.00781289i
$914$	35.2833	−	16.6336i	1.16707	−	0.550189i
$915$		0			0
$916$	−11.1801	−	1.87470i	−0.369401	−	0.0619418i
$917$		−	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	$-0.336058\pi$
$920$	2.31049	−	5.12233i	0.0761748	−	0.168878i
$921$		0			0
$922$	−12.5042	−	26.5240i	−0.411803	−	0.873521i
$923$	2.53335	+	14.3673i	0.0833862	+	0.472907i
$924$		0			0
$925$	25.2693	+	21.2034i	0.830849	+	0.697165i
$926$	−9.62614	−	9.54565i	−0.316334	−	0.313689i
$927$		0			0
$928$	28.6825	+	27.5029i	0.941550	+	0.902828i
$929$	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
$932$	−11.4265	+	9.75265i	−0.374288	+	0.319459i
$933$		0			0
$934$	10.3619	−	22.4669i	0.339051	−	0.735140i
$935$	−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	$0.0703628\pi$
$938$	4.41282	+	6.24618i	0.144084	+	0.203945i
$939$		0			0
$940$	4.10099	+	1.45376i	0.133760	+	0.0474165i
$941$	−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	−0.901458	−	0.432868i	$-0.857502\pi$
$947$	−40.4292	+	14.7150i	−1.31377	+	0.478174i	−0.412315	+	0.911042i	$0.635280\pi$
$948$		0			0
$949$	2.08706	−	1.75125i	0.0677488	−	0.0568480i
$950$	52.3471	+	4.35841i	1.69837	+	0.141405i
$951$		0			0
$952$	−0.338964	−	3.38306i	−0.0109859	−	0.109645i
$953$	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
$956$	−8.23629	+	9.98471i	−0.266381	+	0.322929i
$957$		0			0
$958$	−30.4365	−	21.1220i	−0.983360	−	0.682421i
$959$	6.99708	+	2.54673i	0.225947	+	0.0822382i
$960$		0			0
$961$	3.14365	−	17.8285i	0.101408	−	0.575113i
$962$	−10.7878	−	39.5948i	−0.347811	−	1.27659i
$963$		0			0
$964$	1.19604	−	0.703987i	0.0385217	−	0.0226739i
$965$	1.71141	−	2.03958i	0.0550923	−	0.0656565i
$966$		0			0
$967$	−46.0060	+	8.11209i	−1.47945	+	0.260867i	−0.854359	−	0.519683i	$-0.826050\pi$
$967$	−46.0060	+	8.11209i	−1.47945	+	0.260867i	−0.625093	+	0.780550i	$0.714939\pi$
$968$	31.0211	+	2.32071i	0.997056	+	0.0745904i
$969$		0			0
$970$	−0.130142	−	1.41890i	−0.00417862	−	0.0455581i
$971$	−29.3788			−0.942809			−0.471405	−	0.881917i	$-0.656253\pi$
$971$	−29.3788			−0.942809			−0.471405	+	0.881917i	$0.656253\pi$
$972$		0			0
$973$	−4.33784			−0.139065
$974$	0.918347	+	10.0124i	0.0294257	+	0.320819i
$975$		0			0
$976$	−28.4879	−	9.83020i	−0.911875	−	0.314657i
$977$	−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
$980$	−2.07554	−	3.52623i	−0.0663007	−	0.112641i
$981$		0			0
$982$	−7.34331	−	26.9525i	−0.234335	−	0.860089i
$983$	4.54380	−	25.7692i	0.144925	−	0.821909i	−0.822503	−	0.568761i	$-0.807423\pi$
$983$	4.54380	−	25.7692i	0.144925	−	0.821909i	0.967428	−	0.253148i	$-0.0814660\pi$
$984$		0			0
$985$	−3.55193	−	1.29280i	−0.113174	−	0.0411919i
$986$	20.2083	+	14.0239i	0.643563	+	0.446613i
$987$		0			0
$988$	−50.4114	−	41.5839i	−1.60380	−	1.32296i
$989$	−13.7596	+	7.94413i	−0.437531	+	0.252609i
$990$		0			0
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	0.847932	−	0.530105i	$-0.177847\pi$
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	−0.0351178	+	0.999383i	$0.511181\pi$
$992$	−18.5875	−	8.19701i	−0.590154	−	0.260255i
$993$		0			0
$994$	2.31174	+	0.192475i	0.0733241	+	0.00610495i
$995$	−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.143.16		96
3.2	odd	2		108.2.l.a.47.1	yes	96
4.3	odd	2	inner	324.2.l.a.143.3		96
9.2	odd	6		972.2.l.d.107.12		96
9.4	even	3		972.2.l.b.755.7		96
9.5	odd	6		972.2.l.c.755.10		96
9.7	even	3		972.2.l.a.107.5		96
12.11	even	2		108.2.l.a.47.14	yes	96
27.4	even	9		108.2.l.a.23.14	yes	96
27.5	odd	18		972.2.l.b.215.9		96
27.13	even	9		972.2.l.d.863.3		96
27.14	odd	18		972.2.l.a.863.14		96
27.22	even	9		972.2.l.c.215.8		96
27.23	odd	18	inner	324.2.l.a.179.3		96
36.7	odd	6		972.2.l.a.107.14		96
36.11	even	6		972.2.l.d.107.3		96
36.23	even	6		972.2.l.c.755.8		96
36.31	odd	6		972.2.l.b.755.9		96
108.23	even	18	inner	324.2.l.a.179.16		96
108.31	odd	18		108.2.l.a.23.1	✓	96
108.59	even	18		972.2.l.b.215.7		96
108.67	odd	18		972.2.l.d.863.12		96
108.95	even	18		972.2.l.a.863.5		96
108.103	odd	18		972.2.l.c.215.10		96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.40830 - 0.129170i) q^{2} +(1.96663 - 0.363822i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(0.312070 - 0.371910i) q^{7} +(2.72261 - 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(-0.00722947 + 0.0410004i) q^{11} +(4.05761 + 1.47685i) q^{13} +(0.391449 - 0.564072i) q^{14} +(3.73527 - 1.43101i) q^{16} +(2.14427 - 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.566662 + 0.211653i) q^{20} +(-0.00488525 + 0.0586748i) q^{22} +(-5.03199 + 4.22234i) q^{23} +(-4.61250 + 1.67881i) q^{25} +(5.90510 + 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(2.40260 + 6.60109i) q^{29} +(-2.30836 - 2.75099i) q^{31} +(5.07554 - 2.49778i) q^{32} +(2.85987 - 2.02045i) q^{34} +(-0.0734187 + 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-9.71770 - 4.48186i) q^{38} +(-0.770692 + 0.371267i) q^{40} +(-2.16312 + 5.94312i) q^{41} +(2.38200 + 0.420011i) q^{43} +(0.000699143 + 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(-5.51016 - 4.62358i) q^{47} +(1.17461 + 6.66153i) q^{49} +(-6.27895 + 2.96008i) q^{50} +(8.51712 + 1.42817i) q^{52} -9.90799i q^{53} -0.0125918i q^{55} +(0.564613 - 1.25174i) q^{56} +(4.23625 + 8.98598i) q^{58} +(0.755918 + 4.28703i) q^{59} +(-5.77142 - 4.84280i) q^{61} +(-3.60621 - 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-1.28614 - 0.226781i) q^{65} +(-3.80965 + 10.4669i) q^{67} +(3.76658 - 3.21481i) q^{68} +(-0.0869698 + 0.188570i) q^{70} +(1.68932 + 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(-5.48386 - 7.76221i) q^{74} +(-14.2644 - 5.05658i) q^{76} +(0.0129924 + 0.0154837i) q^{77} +(1.03548 + 2.84496i) q^{79} +(-1.03741 + 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(5.41059 - 1.96930i) q^{83} +(-0.573662 + 0.481360i) q^{85} +(3.40883 + 0.283818i) q^{86} +(0.0117397 + 0.117169i) q^{88} +(-9.00521 - 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(-8.35988 + 10.1345i) q^{92} +(-8.35720 - 5.79964i) q^{94} +(2.15063 + 0.782765i) q^{95} +(-0.578459 + 3.28061i) q^{97} +(2.51468 + 9.22972i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 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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