LMFDB - Embedded newform 324.2.p.a.275.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			275.52
Character	$\chi$	$=$	324.275
Dual form			324.2.p.a.119.52

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40955 + 0.114795i) q^{2} +(-0.807404 + 1.53235i) q^{3} +(1.97364 + 0.323618i) q^{4} +(1.37664 + 0.593826i) q^{5} +(-1.31398 + 2.06723i) q^{6} +(0.328117 - 0.0191107i) q^{7} +(2.74479 + 0.682720i) q^{8} +(-1.69620 - 2.47445i) q^{9} +O(q^{10})$	\(q+(1.40955 + 0.114795i) q^{2} +(-0.807404 + 1.53235i) q^{3} +(1.97364 + 0.323618i) q^{4} +(1.37664 + 0.593826i) q^{5} +(-1.31398 + 2.06723i) q^{6} +(0.328117 - 0.0191107i) q^{7} +(2.74479 + 0.682720i) q^{8} +(-1.69620 - 2.47445i) q^{9} +(1.87228 + 0.995058i) q^{10} +(-0.378950 + 0.509018i) q^{11} +(-2.08942 + 2.76302i) q^{12} +(-0.663958 + 0.703754i) q^{13} +(0.464690 + 0.0107289i) q^{14} +(-2.02146 + 1.63004i) q^{15} +(3.79054 + 1.27741i) q^{16} +(-2.30514 - 0.406459i) q^{17} +(-2.10681 - 3.68257i) q^{18} +(0.442240 - 0.0779788i) q^{19} +(2.52483 + 1.61751i) q^{20} +(-0.235639 + 0.518221i) q^{21} +(-0.592580 + 0.673983i) q^{22} +(-0.169788 + 2.91515i) q^{23} +(-3.26232 + 3.65476i) q^{24} +(-1.88869 - 2.00189i) q^{25} +(-1.01667 + 0.915755i) q^{26} +(5.16125 - 0.601287i) q^{27} +(0.653771 + 0.0684671i) q^{28} +(-0.405970 - 1.71292i) q^{29} +(-3.03646 + 2.06557i) q^{30} +(-2.24773 - 4.47560i) q^{31} +(5.19631 + 2.23571i) q^{32} +(-0.474028 - 0.991667i) q^{33} +(-3.20254 - 0.837541i) q^{34} +(0.463049 + 0.168536i) q^{35} +(-2.54691 - 5.43261i) q^{36} +(6.68750 - 2.43405i) q^{37} +(0.632309 - 0.0591478i) q^{38} +(-0.542316 - 1.58563i) q^{39} +(3.37319 + 2.56979i) q^{40} +(0.549891 - 0.164626i) q^{41} +(-0.391633 + 0.703406i) q^{42} +(1.06039 - 9.07220i) q^{43} +(-0.912640 + 0.881985i) q^{44} +(-0.865666 - 4.41369i) q^{45} +(-0.573969 + 4.08954i) q^{46} +(2.99380 + 1.50354i) q^{47} +(-5.01795 + 4.77705i) q^{48} +(-6.84537 + 0.800109i) q^{49} +(-2.43239 - 3.03857i) q^{50} +(2.48402 - 3.20411i) q^{51} +(-1.53816 + 1.17409i) q^{52} +(-7.54454 - 4.35584i) q^{53} +(7.34404 - 0.255056i) q^{54} +(-0.823948 + 0.475706i) q^{55} +(0.913662 + 0.171557i) q^{56} +(-0.237575 + 0.740627i) q^{57} +(-0.375598 - 2.46104i) q^{58} +(3.60275 + 4.83934i) q^{59} +(-4.51715 + 2.56295i) q^{60} +(-4.02401 + 2.64663i) q^{61} +(-2.65451 - 6.56660i) q^{62} +(-0.603840 - 0.779495i) q^{63} +(7.06779 + 3.74785i) q^{64} +(-1.33194 + 0.574543i) q^{65} +(-0.554327 - 1.45222i) q^{66} +(3.29362 - 13.8969i) q^{67} +(-4.41799 - 1.54819i) q^{68} +(-4.32994 - 2.61388i) q^{69} +(0.633343 + 0.290715i) q^{70} +(-0.732903 - 0.614979i) q^{71} +(-2.96635 - 7.94989i) q^{72} +(8.47993 - 7.11550i) q^{73} +(9.70577 - 2.66322i) q^{74} +(4.59254 - 1.27780i) q^{75} +(0.898060 - 0.0107855i) q^{76} +(-0.114612 + 0.174260i) q^{77} +(-0.582397 - 2.29727i) q^{78} +(-11.2910 - 3.38029i) q^{79} +(4.45967 + 4.00947i) q^{80} +(-3.24583 + 8.39432i) q^{81} +(0.793995 - 0.168924i) q^{82} +(-4.80659 + 16.0551i) q^{83} +(-0.632773 + 0.946526i) q^{84} +(-2.93199 - 1.92840i) q^{85} +(2.53611 - 12.6660i) q^{86} +(2.95258 + 0.760931i) q^{87} +(-1.38766 + 1.13843i) q^{88} +(-4.53781 - 5.40795i) q^{89} +(-0.713526 - 6.32067i) q^{90} +(-0.204407 + 0.243603i) q^{91} +(-1.27850 + 5.69851i) q^{92} +(8.67302 + 0.169306i) q^{93} +(4.04730 + 2.46299i) q^{94} +(0.655113 + 0.155265i) q^{95} +(-7.62141 + 6.15744i) q^{96} +(4.10930 + 9.52643i) q^{97} +(-9.74072 + 0.341976i) q^{98} +(1.90231 + 0.0742983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{5}{54}\right)$

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 $

$2$	1.40955	+	0.114795i	0.996700	+	0.0811724i
$2$	1.40955	+	0.114795i	0.996700	+	0.0811724i
$3$	−0.807404	+	1.53235i	−0.466155	+	0.884703i
$3$	−0.807404	+	1.53235i	−0.466155	+	0.884703i
$4$	1.97364	+	0.323618i	0.986822	+	0.161809i
$5$	1.37664	+	0.593826i	0.615654	+	0.265567i	0.680986	−	0.732296i	$-0.261551\pi$
$5$	1.37664	+	0.593826i	0.615654	+	0.265567i	−0.0653320	+	0.997864i	$0.520811\pi$
$6$	−1.31398	+	2.06723i	−0.536430	+	0.843945i
$7$	0.328117	−	0.0191107i	0.124017	−	0.00722315i	0.00397578	−	0.999992i	$-0.498734\pi$
$7$	0.328117	−	0.0191107i	0.124017	−	0.00722315i	0.120041	+	0.992769i	$0.461697\pi$
$8$	2.74479	+	0.682720i	0.970431	+	0.241378i
$9$	−1.69620	−	2.47445i	−0.565399	−	0.824817i
$10$	1.87228	+	0.995058i	0.592066	+	0.314665i
$11$	−0.378950	+	0.509018i	−0.114258	+	0.153475i	−0.855573	−	0.517682i	$-0.826795\pi$
$11$	−0.378950	+	0.509018i	−0.114258	+	0.153475i	0.741315	+	0.671157i	$0.234202\pi$
$12$	−2.08942	+	2.76302i	−0.603165	+	0.797616i
$13$	−0.663958	+	0.703754i	−0.184149	+	0.195186i	−0.812871	−	0.582444i	$-0.802097\pi$
$13$	−0.663958	+	0.703754i	−0.184149	+	0.195186i	0.628722	+	0.777630i	$0.283578\pi$
$14$	0.464690	+	0.0107289i	0.124194	+	0.00286742i
$15$	−2.02146	+	1.63004i	−0.521938	+	0.420876i
$16$	3.79054	+	1.27741i	0.947636	+	0.319354i
$17$	−2.30514	−	0.406459i	−0.559079	−	0.0985807i	−0.113034	−	0.993591i	$-0.536057\pi$
$17$	−2.30514	−	0.406459i	−0.559079	−	0.0985807i	−0.446045	+	0.895010i	$0.647168\pi$
$18$	−2.10681	−	3.68257i	−0.496581	−	0.867990i
$19$	0.442240	−	0.0779788i	0.101457	−	0.0178896i	−0.122689	−	0.992445i	$-0.539152\pi$
$19$	0.442240	−	0.0779788i	0.101457	−	0.0178896i	0.224146	+	0.974556i	$0.428041\pi$
$20$	2.52483	+	1.61751i	0.564570	+	0.361686i
$21$	−0.235639	+	0.518221i	−0.0514206	+	0.113085i
$22$	−0.592580	+	0.673983i	−0.126339	+	0.143694i
$23$	−0.169788	+	2.91515i	−0.0354032	+	0.607850i	0.933218	+	0.359310i	$0.116988\pi$
$23$	−0.169788	+	2.91515i	−0.0354032	+	0.607850i	−0.968622	+	0.248540i	$0.920049\pi$
$24$	−3.26232	+	3.65476i	−0.665919	+	0.746024i
$25$	−1.88869	−	2.00189i	−0.377738	−	0.400378i
$26$	−1.01667	+	0.915755i	−0.199385	+	0.179594i
$27$	5.16125	−	0.601287i	0.993282	−	0.115718i
$28$	0.653771	+	0.0684671i	0.123551	+	0.0129391i
$29$	−0.405970	−	1.71292i	−0.0753867	−	0.318081i	0.922266	−	0.386555i	$-0.126335\pi$
$29$	−0.405970	−	1.71292i	−0.0753867	−	0.318081i	−0.997653	+	0.0684739i	$0.978187\pi$
$30$	−3.03646	+	2.06557i	−0.554380	+	0.377120i
$31$	−2.24773	−	4.47560i	−0.403705	−	0.803842i	−0.999999	−	0.00107646i	$-0.999657\pi$
$31$	−2.24773	−	4.47560i	−0.403705	−	0.803842i	0.596295	−	0.802766i	$-0.296639\pi$
$32$	5.19631	+	2.23571i	0.918586	+	0.395222i
$33$	−0.474028	−	0.991667i	−0.0825178	−	0.172627i
$34$	−3.20254	−	0.837541i	−0.549232	−	0.143637i
$35$	0.463049	+	0.168536i	0.0782696	+	0.0284878i
$36$	−2.54691	−	5.43261i	−0.424485	−	0.905435i
$37$	6.68750	−	2.43405i	1.09942	−	0.400156i	0.272317	−	0.962208i	$-0.412210\pi$
$37$	6.68750	−	2.43405i	1.09942	−	0.400156i	0.827102	+	0.562052i	$0.189988\pi$
$38$	0.632309	−	0.0591478i	0.102574	−	0.00959504i
$39$	−0.542316	−	1.58563i	−0.0868400	−	0.253904i
$40$	3.37319	+	2.56979i	0.533348	+	0.406320i
$41$	0.549891	−	0.164626i	0.0858785	−	0.0257103i	−0.243576	−	0.969882i	$-0.578320\pi$
$41$	0.549891	−	0.164626i	0.0858785	−	0.0257103i	0.329454	+	0.944172i	$0.393135\pi$
$42$	−0.391633	+	0.703406i	−0.0604304	+	0.108538i
$43$	1.06039	−	9.07220i	0.161708	−	1.38350i	−0.631891	−	0.775057i	$-0.717721\pi$
$43$	1.06039	−	9.07220i	0.161708	−	1.38350i	0.793599	−	0.608441i	$-0.208205\pi$
$44$	−0.912640	+	0.881985i	−0.137586	+	0.132964i
$45$	−0.865666	−	4.41369i	−0.129046	−	0.657954i
$46$	−0.573969	+	4.08954i	−0.0846271	+	0.602970i
$47$	2.99380	+	1.50354i	0.436691	+	0.219314i	0.653542	−	0.756890i	$-0.273282\pi$
$47$	2.99380	+	1.50354i	0.436691	+	0.219314i	−0.216851	+	0.976205i	$0.569579\pi$
$48$	−5.01795	+	4.77705i	−0.724278	+	0.689508i
$49$	−6.84537	+	0.800109i	−0.977910	+	0.114301i
$50$	−2.43239	−	3.03857i	−0.343991	−	0.429719i
$51$	2.48402	−	3.20411i	0.347832	−	0.448665i
$52$	−1.53816	+	1.17409i	−0.213305	+	0.162817i
$53$	−7.54454	−	4.35584i	−1.03632	−	0.598321i	−0.117533	−	0.993069i	$-0.537499\pi$
$53$	−7.54454	−	4.35584i	−1.03632	−	0.598321i	−0.918790	+	0.394748i	$0.870832\pi$
$54$	7.34404	−	0.255056i	0.999397	−	0.0347087i
$55$	−0.823948	+	0.475706i	−0.111101	+	0.0641442i
$56$	0.913662	+	0.171557i	0.122093	+	0.0229253i
$57$	−0.237575	+	0.740627i	−0.0314676	+	0.0980985i
$58$	−0.375598	−	2.46104i	−0.0493184	−	0.323151i
$59$	3.60275	+	4.83934i	0.469039	+	0.630028i	0.972197	−	0.234166i	$-0.0752360\pi$
$59$	3.60275	+	4.83934i	0.469039	+	0.630028i	−0.503158	+	0.864194i	$0.667829\pi$
$60$	−4.51715	+	2.56295i	−0.583162	+	0.330875i
$61$	−4.02401	+	2.64663i	−0.515221	+	0.338866i	−0.780346	−	0.625348i	$-0.784957\pi$
$61$	−4.02401	+	2.64663i	−0.515221	+	0.338866i	0.265125	+	0.964214i	$0.414587\pi$
$62$	−2.65451	−	6.56660i	−0.337123	−	0.833959i
$63$	−0.603840	−	0.779495i	−0.0760767	−	0.0982072i
$64$	7.06779	+	3.74785i	0.883473	+	0.468481i
$65$	−1.33194	+	0.574543i	−0.165207	+	0.0712633i
$66$	−0.554327	−	1.45222i	−0.0682329	−	0.178756i
$67$	3.29362	−	13.8969i	0.402380	−	1.69778i	−0.274421	−	0.961610i	$-0.588486\pi$
$67$	3.29362	−	13.8969i	0.402380	−	1.69778i	0.676801	−	0.736166i	$-0.263366\pi$
$68$	−4.41799	−	1.54819i	−0.535760	−	0.187746i
$69$	−4.32994	−	2.61388i	−0.521263	−	0.314674i
$70$	0.633343	+	0.290715i	0.0756989	+	0.0347471i
$71$	−0.732903	−	0.614979i	−0.0869796	−	0.0729845i	0.598261	−	0.801301i	$-0.295859\pi$
$71$	−0.732903	−	0.614979i	−0.0869796	−	0.0729845i	−0.685241	+	0.728317i	$0.740303\pi$
$72$	−2.96635	−	7.94989i	−0.349588	−	0.936903i
$73$	8.47993	−	7.11550i	0.992500	−	0.832807i	0.00657250	−	0.999978i	$-0.497908\pi$
$73$	8.47993	−	7.11550i	0.992500	−	0.832807i	0.985928	+	0.167172i	$0.0534634\pi$
$74$	9.70577	−	2.66322i	1.12827	−	0.309593i
$75$	4.59254	−	1.27780i	0.530300	−	0.147547i
$76$	0.898060	−	0.0107855i	0.103015	−	0.00123718i
$77$	−0.114612	+	0.174260i	−0.0130613	+	0.0198587i
$78$	−0.582397	−	2.29727i	−0.0659435	−	0.260115i
$79$	−11.2910	−	3.38029i	−1.27033	−	0.380313i	−0.420465	−	0.907309i	$-0.638133\pi$
$79$	−11.2910	−	3.38029i	−1.27033	−	0.380313i	−0.849868	+	0.526996i	$0.823318\pi$
$80$	4.45967	+	4.00947i	0.498606	+	0.448272i
$81$	−3.24583	+	8.39432i	−0.360648	+	0.932702i
$82$	0.793995	−	0.168924i	0.0876821	−	0.0186545i
$83$	−4.80659	+	16.0551i	−0.527591	+	1.76228i	0.112153	+	0.993691i	$0.464225\pi$
$83$	−4.80659	+	16.0551i	−0.527591	+	1.76228i	−0.639745	+	0.768587i	$0.720960\pi$
$84$	−0.632773	+	0.946526i	−0.0690412	+	0.103274i
$85$	−2.93199	−	1.92840i	−0.318019	−	0.209165i
$86$	2.53611	−	12.6660i	0.273476	−	1.36581i
$87$	2.95258	+	0.760931i	0.316549	+	0.0815804i
$88$	−1.38766	+	1.13843i	−0.147925	+	0.121357i
$89$	−4.53781	−	5.40795i	−0.481007	−	0.573242i	0.469900	−	0.882720i	$-0.344290\pi$
$89$	−4.53781	−	5.40795i	−0.481007	−	0.573242i	−0.950907	+	0.309478i	$0.899846\pi$
$90$	−0.713526	−	6.32067i	−0.0752123	−	0.666258i
$91$	−0.204407	+	0.243603i	−0.0214277	+	0.0255365i
$92$	−1.27850	+	5.69851i	−0.133292	+	0.594111i
$93$	8.67302	+	0.169306i	0.899350	+	0.0175562i
$94$	4.04730	+	2.46299i	0.417448	+	0.254038i
$95$	0.655113	+	0.155265i	0.0672132	+	0.0159298i
$96$	−7.62141	+	6.15744i	−0.777857	+	0.628441i
$97$	4.10930	+	9.52643i	0.417236	+	0.967262i	0.989145	+	0.146945i	$0.0469439\pi$
$97$	4.10930	+	9.52643i	0.417236	+	0.967262i	−0.571909	+	0.820317i	$0.693797\pi$
$98$	−9.74072	+	0.341976i	−0.983961	+	0.0345448i
$99$	1.90231	+	0.0742983i	0.191190	+	0.00746726i
$100$	−3.07975	−	4.56224i	−0.307975	−	0.456224i
$101$	6.73379	+	10.2382i	0.670037	+	1.01874i	0.997273	+	0.0737992i	$0.0235124\pi$
$101$	6.73379	+	10.2382i	0.670037	+	1.01874i	−0.327236	+	0.944943i	$0.606117\pi$
$102$	3.86915	−	4.23119i	0.383103	−	0.418950i
$103$	−10.2635	+	7.64089i	−1.01129	+	0.752880i	−0.969210	−	0.246235i	$-0.920807\pi$
$103$	−10.2635	+	7.64089i	−1.01129	+	0.752880i	−0.0420826	+	0.999114i	$0.513399\pi$
$104$	−2.30289	+	1.47836i	−0.225817	+	0.144965i
$105$	−0.632124	+	0.573477i	−0.0616890	+	0.0559656i
$106$	−10.1344	−	7.00584i	−0.984336	−	0.680468i
$107$	5.80637	+	10.0569i	0.561323	+	0.972240i	0.997381	+	0.0723219i	$0.0230409\pi$
$107$	5.80637	+	10.0569i	0.561323	+	0.972240i	−0.436058	+	0.899919i	$0.643626\pi$
$108$	10.3810	+	0.483547i	0.998917	+	0.0465294i
$109$	8.15040	−	14.1169i	0.780666	−	1.35215i	−0.150888	−	0.988551i	$-0.548213\pi$
$109$	8.15040	−	14.1169i	0.780666	−	1.35215i	0.931554	−	0.363603i	$-0.118453\pi$
$110$	−1.21600	+	0.575945i	−0.115941	+	0.0549142i
$111$	−1.66970	+	12.2129i	−0.158480	+	1.15919i
$112$	1.26815	+	0.346702i	0.119829	+	0.0327603i
$113$	1.90325	+	16.2834i	0.179043	+	1.53181i	0.721906	+	0.691991i	$0.243266\pi$
$113$	1.90325	+	16.2834i	0.179043	+	1.53181i	−0.542863	+	0.839821i	$0.682660\pi$
$114$	−0.419894	+	1.01668i	−0.0393267	+	0.0952204i
$115$	−1.96483	+	3.91230i	−0.183221	+	0.364823i
$116$	−0.246907	−	3.51207i	−0.0229247	−	0.326088i
$117$	2.86761	+	0.449226i	0.265111	+	0.0415309i
$118$	4.52272	+	7.23485i	0.416350	+	0.666022i
$119$	−0.764124	−	0.0893133i	−0.0700472	−	0.00818734i
$120$	−6.66135	+	3.09405i	−0.608095	+	0.282446i
$121$	3.03934	+	10.1521i	0.276304	+	0.922918i
$122$	−5.97585	+	3.26861i	−0.541028	+	0.295926i
$123$	−0.191718	+	0.975546i	−0.0172867	+	0.0879620i
$124$	−2.98784	−	9.56065i	−0.268316	−	0.858572i
$125$	−3.97516	−	10.9217i	−0.355549	−	0.976863i
$126$	−0.761659	−	1.16805i	−0.0678539	−	0.104058i
$127$	1.25262	−	3.44155i	0.111152	−	0.305388i	−0.871628	−	0.490169i	$-0.836935\pi$
$127$	1.25262	−	3.44155i	0.111152	−	0.305388i	0.982780	+	0.184781i	$0.0591574\pi$
$128$	9.53214	+	6.09412i	0.842530	+	0.538649i
$129$	13.0456	+	8.94982i	1.14860	+	0.787988i
$130$	−1.94339	+	0.656945i	−0.170446	+	0.0576179i
$131$	−14.4833	+	7.27379i	−1.26541	+	0.635514i	−0.949646	−	0.313323i	$-0.898558\pi$
$131$	−14.4833	+	7.27379i	−1.26541	+	0.635514i	−0.315766	+	0.948837i	$0.602261\pi$
$132$	−0.614642	−	2.11060i	−0.0534977	−	0.183704i
$133$	0.143616	−	0.0340377i	0.0124531	−	0.00295144i
$134$	6.23781	−	19.2102i	0.538865	−	1.65951i
$135$	7.46226	+	2.23713i	0.642249	+	0.192541i
$136$	−6.04964	−	2.68941i	−0.518752	−	0.230615i
$137$	−3.89090	+	3.67088i	−0.332422	+	0.313624i	−0.834296	−	0.551317i	$-0.814126\pi$
$137$	−3.89090	+	3.67088i	−0.332422	+	0.313624i	0.501874	+	0.864941i	$0.332644\pi$
$138$	−5.80319	−	4.18144i	−0.494000	−	0.355947i
$139$	−3.66324	−	0.213359i	−0.310712	−	0.0180969i	−0.0979193	−	0.995194i	$-0.531219\pi$
$139$	−3.66324	−	0.213359i	−0.310712	−	0.0180969i	−0.212792	+	0.977097i	$0.568256\pi$
$140$	0.859353	+	0.482482i	0.0726286	+	0.0407771i
$141$	−4.72117	+	3.37359i	−0.397594	+	0.284107i
$142$	−0.962464	−	0.950975i	−0.0807682	−	0.0798040i
$143$	−0.106617	−	0.604654i	−0.00891574	−	0.0505637i
$144$	−3.26861	−	11.5463i	−0.272384	−	0.962189i
$145$	0.458302	−	2.59916i	0.0380599	−	0.215848i
$146$	12.7697	−	9.05618i	1.05683	−	0.749495i
$147$	4.30093	−	11.1355i	0.354735	−	0.918442i
$148$	13.9865	−	2.63975i	1.14968	−	0.216986i
$149$	6.45387	+	6.08892i	0.528722	+	0.498823i	0.903674	−	0.428221i	$-0.140859\pi$
$149$	6.45387	+	6.08892i	0.528722	+	0.498823i	−0.374952	+	0.927044i	$0.622341\pi$
$150$	6.62008	−	1.27391i	0.540527	−	0.104015i
$151$	−7.56496	−	5.63191i	−0.615628	−	0.458318i	0.243625	−	0.969870i	$-0.421664\pi$
$151$	−7.56496	−	5.63191i	−0.615628	−	0.458318i	−0.859253	+	0.511551i	$0.829071\pi$
$152$	1.26710	+	0.0878902i	0.102775	+	0.00712884i
$153$	2.90421	+	6.39340i	0.234792	+	0.516875i
$154$	−0.181556	+	0.232470i	−0.0146302	+	0.0187330i
$155$	−0.436597	−	7.49608i	−0.0350683	−	0.602099i
$156$	−0.557200	−	3.30497i	−0.0446117	−	0.264610i
$157$	−0.286973	+	0.665278i	−0.0229029	+	0.0530950i	−0.929284	−	0.369367i	$-0.879575\pi$
$157$	−0.286973	+	0.665278i	−0.0229029	+	0.0530950i	0.906381	+	0.422462i	$0.138834\pi$
$158$	−15.5271	−	6.06083i	−1.23527	−	0.482174i
$159$	12.7662	−	8.04396i	1.01242	−	0.637928i
$160$	5.82584	+	6.16348i	0.460573	+	0.487266i
$161$			0.959755i			0.0756393i
$162$	−5.53877	+	11.4596i	−0.435167	+	0.900350i
$163$		−	6.29300i		−	0.492906i	−0.969155	−	0.246453i	$-0.920735\pi$
$163$		−	6.29300i		−	0.492906i	0.969155	−	0.246453i	$-0.0792651\pi$
$164$	1.13856	−	0.146959i	0.0889070	−	0.0114756i
$165$	−0.0636904	−	1.64666i	−0.00495829	−	0.128193i
$166$	−8.61816	+	22.0787i	−0.668899	+	1.71364i
$167$	0.304123	−	0.705036i	0.0235337	−	0.0545573i	−0.906044	−	0.423184i	$-0.860913\pi$
$167$	0.304123	−	0.705036i	0.0235337	−	0.0545573i	0.929578	+	0.368626i	$0.120172\pi$
$168$	−1.00058	+	1.26153i	−0.0771964	+	0.0973295i
$169$	0.701453	+	12.0435i	0.0539579	+	0.926422i
$170$	−3.91141	−	3.05475i	−0.299992	−	0.234289i
$171$	−0.943081	−	0.962034i	−0.0721192	−	0.0735686i
$172$	5.02876	−	17.5621i	0.383439	−	1.33910i
$173$	2.61957	+	1.95020i	0.199162	+	0.148271i	0.692120	−	0.721782i	$-0.256677\pi$
$173$	2.61957	+	1.95020i	0.199162	+	0.148271i	−0.492958	+	0.870053i	$0.664084\pi$
$174$	4.07444	+	1.41151i	0.308883	+	0.107006i
$175$	−0.657969	−	0.620761i	−0.0497378	−	0.0469252i
$176$	−2.08665	+	1.44538i	−0.157287	+	0.108949i
$177$	−10.3244	+	1.61338i	−0.776033	+	0.121269i
$178$	−5.77545	−	8.14368i	−0.432888	−	0.610395i
$179$	1.91261	−	10.8469i	0.142955	−	0.810739i	−0.826031	−	0.563625i	$-0.809407\pi$
$179$	1.91261	−	10.8469i	0.142955	−	0.810739i	0.968986	−	0.247115i	$-0.0794824\pi$
$180$	−0.280166	−	8.99120i	−0.0208823	−	0.670164i
$181$	−0.243074	−	1.37854i	−0.0180675	−	0.102466i	0.974440	−	0.224646i	$-0.0721226\pi$
$181$	−0.243074	−	1.37854i	−0.0180675	−	0.102466i	−0.992508	+	0.122180i	$0.961011\pi$
$182$	−0.316085	+	0.319904i	−0.0234298	+	0.0237129i
$183$	−0.806568	−	8.30309i	−0.0596232	−	0.613782i
$184$	−2.45626	+	7.88556i	−0.181078	+	0.581331i
$185$	10.6517	+	0.620392i	0.783130	+	0.0456121i
$186$	12.2056	+	1.23427i	0.894958	+	0.0905007i
$187$	1.08043	−	1.01933i	0.0790087	−	0.0745409i
$188$	5.42213	+	3.93631i	0.395449	+	0.287085i
$189$	1.68200	−	0.295927i	0.122348	−	0.0215255i
$190$	0.905589	+	0.294057i	0.0656983	+	0.0213331i
$191$	−19.4895	+	4.61909i	−1.41021	+	0.334226i	−0.864029	−	0.503442i	$-0.832067\pi$
$191$	−19.4895	+	4.61909i	−1.41021	+	0.334226i	−0.546180	+	0.837668i	$0.683919\pi$
$192$	−11.4496	+	7.80430i	−0.826302	+	0.563227i
$193$	−7.21845	+	3.62524i	−0.519595	+	0.260951i	−0.689212	−	0.724560i	$-0.742043\pi$
$193$	−7.21845	+	3.62524i	−0.519595	+	0.260951i	0.169617	+	0.985510i	$0.445747\pi$
$194$	4.69866	+	13.8997i	0.337344	+	0.997938i
$195$	0.195013	−	2.50489i	0.0139652	−	0.179379i
$196$	−13.7693	−	0.636157i	−0.983519	−	0.0454398i
$197$	6.70382	−	18.4186i	0.477627	−	1.31227i	−0.433874	−	0.900973i	$-0.642854\pi$
$197$	6.70382	−	18.4186i	0.477627	−	1.31227i	0.911502	−	0.411297i	$-0.134924\pi$
$198$	2.67287	+	0.323103i	0.189953	+	0.0229620i
$199$	6.39423	+	17.5680i	0.453275	+	1.24536i	0.930406	+	0.366531i	$0.119455\pi$
$199$	6.39423	+	17.5680i	0.453275	+	1.24536i	−0.477131	+	0.878832i	$0.658323\pi$
$200$	−3.81733	−	6.78423i	−0.269926	−	0.479717i
$201$	18.6356	+	16.2674i	1.31446	+	1.14741i
$202$	8.31629	+	15.2043i	0.585132	+	1.06977i
$203$	−0.165941	−	0.554280i	−0.0116468	−	0.0389029i
$204$	5.93947	−	5.51990i	0.415846	−	0.386470i
$205$	0.854764	+	0.0999075i	0.0596993	+	0.00697785i
$206$	−15.3440	+	9.59200i	−1.06907	+	0.668306i
$207$	7.50138	−	4.52453i	0.521382	−	0.314477i
$208$	−3.41575	+	1.81946i	−0.236839	+	0.126157i
$209$	−0.127894	+	0.254658i	−0.00884662	+	0.0176151i
$210$	−0.956841	+	0.735778i	−0.0660283	+	0.0507735i
$211$	2.48946	+	21.2987i	0.171382	+	1.46626i	0.755795	+	0.654809i	$0.227251\pi$
$211$	2.48946	+	21.2987i	0.171382	+	1.46626i	−0.584413	+	0.811456i	$0.698675\pi$
$212$	−13.4806	−	11.0384i	−0.925852	−	0.758123i
$213$	1.53411	−	0.626528i	0.105116	−	0.0429290i
$214$	7.02987	+	14.8423i	0.480552	+	1.01460i
$215$	6.84709	−	11.8595i	0.466968	−	0.808812i
$216$	14.5771	+	1.87328i	0.991844	+	0.127460i
$217$	−0.823052	−	1.42557i	−0.0558724	−	0.0967738i
$218$	13.1089	−	18.9628i	0.887848	−	1.28432i
$219$	4.05672	+	18.7393i	0.274128	+	1.26629i
$220$	−1.78013	+	0.672231i	−0.120016	+	0.0453218i
$221$	1.81656	−	1.35238i	0.122195	−	0.0909710i
$222$	−3.75549	+	17.0229i	−0.252052	+	1.14250i
$223$	13.7455	+	20.8991i	0.920470	+	1.39951i	0.916727	+	0.399513i	$0.130821\pi$
$223$	13.7455	+	20.8991i	0.920470	+	1.39951i	0.00374240	+	0.999993i	$0.498809\pi$
$224$	1.74772	+	0.634271i	0.116775	+	0.0423790i
$225$	−1.75000	+	8.06907i	−0.116667	+	0.537938i
$226$	0.813473	+	23.1707i	0.0541114	+	1.54129i
$227$	−2.34698	−	5.44092i	−0.155775	−	0.361126i	0.822400	−	0.568909i	$-0.192634\pi$
$227$	−2.34698	−	5.44092i	−0.155775	−	0.361126i	−0.978175	+	0.207783i	$0.933375\pi$
$228$	−0.708570	+	1.38485i	−0.0469262	+	0.0917140i
$229$	−1.40972	−	0.334110i	−0.0931571	−	0.0220786i	0.183773	−	0.982969i	$-0.441169\pi$
$229$	−1.40972	−	0.334110i	−0.0931571	−	0.0220786i	−0.276930	+	0.960890i	$0.589317\pi$
$230$	−3.21863	+	5.28901i	−0.212230	+	0.348747i
$231$	−0.174488	−	0.316324i	−0.0114805	−	0.0208126i
$232$	0.0551421	−	4.97878i	0.00362026	−	0.326873i
$233$	7.03544	−	8.38451i	0.460907	−	0.549288i	−0.484665	−	0.874700i	$-0.661059\pi$
$233$	7.03544	−	8.38451i	0.460907	−	0.549288i	0.945572	+	0.325412i	$0.105503\pi$
$234$	3.99046	+	0.962392i	0.260865	+	0.0629136i
$235$	3.22856	+	3.84764i	0.210608	+	0.250993i
$236$	5.54446	+	10.7170i	0.360913	+	0.697621i
$237$	14.2962	−	14.5725i	0.928636	−	0.946583i
$238$	−1.06682	−	0.213609i	−0.0691514	−	0.0138462i
$239$	−25.1035	−	16.5108i	−1.62381	−	1.06800i	−0.941544	−	0.336890i	$-0.890625\pi$
$239$	−25.1035	−	16.5108i	−1.62381	−	1.06800i	−0.682265	−	0.731105i	$-0.739005\pi$
$240$	−9.74467	+	3.59651i	−0.629016	+	0.232154i
$241$	−5.35969	+	17.9026i	−0.345248	+	1.15321i	0.592407	+	0.805639i	$0.298178\pi$
$241$	−5.35969	+	17.9026i	−0.345248	+	1.15321i	−0.937654	+	0.347569i	$0.887007\pi$
$242$	3.11868	+	14.6588i	0.200476	+	0.942301i
$243$	−10.2423	−	11.7514i	−0.657047	−	0.753850i
$244$	−8.79846	+	3.92127i	−0.563264	+	0.251033i
$245$	−9.89877	−	2.96350i	−0.632409	−	0.189331i
$246$	−0.382224	+	1.35307i	−0.0243697	+	0.0862685i
$247$	−0.238751	+	0.363003i	−0.0151913	+	0.0230973i
$248$	−3.11398	−	13.8192i	−0.197738	−	0.877519i
$249$	−20.7212	−	20.3283i	−1.31315	−	1.28826i
$250$	−4.34942	−	15.8509i	−0.275082	−	1.00250i
$251$	−11.4708	+	9.62517i	−0.724033	+	0.607536i	−0.928498	−	0.371338i	$-0.878899\pi$
$251$	−11.4708	+	9.62517i	−0.724033	+	0.607536i	0.204465	+	0.978874i	$0.434455\pi$
$252$	−0.939507	−	1.73386i	−0.0591834	−	0.109223i
$253$	−1.41952	−	1.19112i	−0.0892445	−	0.0748850i
$254$	2.16070	−	4.70723i	0.135574	−	0.295358i
$255$	5.32229	−	2.93584i	0.333295	−	0.183850i
$256$	12.7364	+	9.68419i	0.796026	+	0.605262i
$257$	−3.71493	+	15.6745i	−0.231731	+	0.977750i	0.725454	+	0.688271i	$0.241630\pi$
$257$	−3.71493	+	15.6745i	−0.231731	+	0.977750i	−0.957185	+	0.289478i	$0.906518\pi$
$258$	17.3610	+	14.1128i	1.08085	+	0.878622i
$259$	2.14777	−	0.926457i	0.133456	−	0.0575672i
$260$	−2.81471	+	0.702904i	−0.174561	+	0.0435922i
$261$	−3.54993	+	3.91000i	−0.219735	+	0.242023i
$262$	−21.2499	+	8.59013i	−1.31282	+	0.530700i
$263$	20.0884	−	13.2123i	1.23870	−	0.814708i	0.250539	−	0.968107i	$-0.419392\pi$
$263$	20.0884	−	13.2123i	1.23870	−	0.814708i	0.988164	+	0.153399i	$0.0490218\pi$
$264$	−0.624079	−	3.04555i	−0.0384094	−	0.187441i
$265$	−7.79954	−	10.4766i	−0.479122	−	0.643572i
$266$	0.206341	−	0.0314913i	0.0126516	−	0.00193085i
$267$	11.9507	−	2.58712i	0.731373	−	0.158329i
$268$	10.9977	−	26.3616i	0.671793	−	1.61029i
$269$	17.6162	−	10.1707i	1.07408	−	0.620120i	0.144786	−	0.989463i	$-0.453751\pi$
$269$	17.6162	−	10.1707i	1.07408	−	0.620120i	0.929293	+	0.369343i	$0.120417\pi$
$270$	10.2616	+	4.00997i	0.624501	+	0.244039i
$271$	−5.90072	−	3.40678i	−0.358443	−	0.206947i	0.309954	−	0.950751i	$-0.399686\pi$
$271$	−5.90072	−	3.40678i	−0.358443	−	0.206947i	−0.668398	+	0.743804i	$0.733020\pi$
$272$	−8.21852	−	4.48532i	−0.498321	−	0.271962i
$273$	−0.208246	−	0.509909i	−0.0126036	−	0.0308611i
$274$	−5.90581	+	4.72762i	−0.356783	+	0.285606i
$275$	1.73472	−	0.202759i	0.104607	−	0.0122268i
$276$	−7.69986	−	6.56011i	−0.463477	−	0.394872i
$277$	−7.93225	−	3.98372i	−0.476603	−	0.239359i	0.194246	−	0.980953i	$-0.437774\pi$
$277$	−7.93225	−	3.98372i	−0.476603	−	0.239359i	−0.670849	+	0.741594i	$0.734070\pi$
$278$	−5.13901	−	0.721261i	−0.308217	−	0.0432584i
$279$	−7.26207	+	13.1534i	−0.434769	+	0.787474i
$280$	1.15591	+	0.778730i	0.0690789	+	0.0465380i
$281$	−0.319706	+	2.73526i	−0.0190721	+	0.163172i	−0.999418	−	0.0341146i	$-0.989139\pi$
$281$	−0.319706	+	2.73526i	−0.0190721	+	0.163172i	0.980346	+	0.197287i	$0.0632129\pi$
$282$	−7.04197	+	4.21326i	−0.419343	+	0.250896i
$283$	11.0808	−	3.31736i	0.658683	−	0.197197i	0.0600194	−	0.998197i	$-0.480884\pi$
$283$	11.0808	−	3.31736i	0.658683	−	0.197197i	0.598664	+	0.801000i	$0.295699\pi$
$284$	−1.24747	−	1.45093i	−0.0740238	−	0.0860968i
$285$	−0.766861	+	0.878502i	−0.0454249	+	0.0520379i
$286$	−0.0808700	−	0.864527i	−0.00478194	−	0.0511206i
$287$	0.177283	−	0.0645256i	0.0104647	−	0.00380882i
$288$	−3.28180	−	16.6502i	−0.193382	−	0.981124i
$289$	−10.8263	−	3.94045i	−0.636842	−	0.231791i
$290$	0.944368	−	3.61102i	0.0554552	−	0.212047i
$291$	−17.9157	−	1.39479i	−1.05024	−	0.0817639i
$292$	19.0391	−	11.2992i	1.11418	−	0.661236i
$293$	−8.47008	−	16.8653i	−0.494827	−	0.985282i	−0.992990	−	0.118198i	$-0.962288\pi$
$293$	−8.47008	−	16.8653i	−0.494827	−	0.985282i	0.498163	−	0.867083i	$-0.334008\pi$
$294$	7.34067	−	15.2023i	0.428117	−	0.886617i
$295$	2.08598	+	8.80146i	0.121451	+	0.512441i
$296$	20.0176	−	2.11528i	1.16350	−	0.122948i
$297$	−1.64979	+	2.85502i	−0.0957304	+	0.165665i
$298$	8.39806	+	9.32348i	0.486486	+	0.540095i
$299$	−1.93881	−	2.05502i	−0.112125	−	0.118845i
$300$	9.47755	−	1.03569i	0.547187	−	0.0597954i
$301$	0.174556	−	2.99701i	0.0100612	−	0.172745i
$302$	−10.0167	−	8.80686i	−0.576394	−	0.506778i
$303$	−21.1254	+	2.05214i	−1.21363	+	0.117892i
$304$	1.77594	+	0.269342i	0.101857	+	0.0154478i
$305$	−7.11127	+	1.25391i	−0.407190	+	0.0717986i
$306$	3.35969	+	9.34518i	0.192061	+	0.534228i
$307$	10.2906	+	1.81451i	0.587315	+	0.103560i	0.459406	−	0.888226i	$-0.348062\pi$
$307$	10.2906	+	1.81451i	0.587315	+	0.103560i	0.127909	+	0.991786i	$0.459173\pi$
$308$	−0.282598	+	0.306836i	−0.0161025	+	0.0174836i
$309$	−3.42174	−	21.8966i	−0.194656	−	1.24565i
$310$	0.245110	−	10.6162i	0.0139213	−	0.602959i
$311$	19.0200	−	20.1600i	1.07852	−	1.14317i	0.0894139	−	0.995995i	$-0.471501\pi$
$311$	19.0200	−	20.1600i	1.07852	−	1.14317i	0.989111	−	0.147175i	$-0.0470179\pi$
$312$	−0.406004	−	4.72248i	−0.0229855	−	0.267358i
$313$	9.50406	−	12.7662i	0.537201	−	0.721587i	−0.447800	−	0.894134i	$-0.647792\pi$
$313$	9.50406	−	12.7662i	0.537201	−	0.721587i	0.985001	+	0.172547i	$0.0551997\pi$
$314$	−0.480872	+	0.904797i	−0.0271372	+	0.0510607i
$315$	−0.368388	−	1.43166i	−0.0207563	−	0.0806651i
$316$	−21.1904	−	10.3255i	−1.19205	−	0.580852i
$317$	−20.1100	+	1.17127i	−1.12949	+	0.0657852i	−0.612691	−	0.790323i	$-0.709913\pi$
$317$	−20.1100	+	1.17127i	−1.12949	+	0.0657852i	−0.516797	+	0.856108i	$0.672876\pi$
$318$	18.9179	−	9.87284i	1.06086	−	0.553642i
$319$	1.02575	+	0.442465i	0.0574309	+	0.0247733i
$320$	7.50426	+	9.35650i	0.419501	+	0.523044i
$321$	−20.0988	+	0.777392i	−1.12181	+	0.0433898i
$322$	−0.110175	+	1.35282i	−0.00613982	+	0.0753897i
$323$	−1.05112			−0.0584859
$324$	−9.12267	+	15.5170i	−0.506815	+	0.862055i
$325$	2.66285			0.147708
$326$	0.722406	−	8.87028i	0.0400104	−	0.491279i
$327$	15.0514	+	23.8873i	0.832343	+	1.32097i
$328$	1.62173	−	0.0764444i	0.0895451	−	0.00422093i
$329$	1.01105	+	0.436125i	0.0557411	+	0.0240444i
$330$	0.0992545	−	2.32836i	0.00546378	−	0.128172i
$331$	7.33406	−	0.427160i	0.403116	−	0.0234788i	0.144611	−	0.989489i	$-0.453807\pi$
$331$	7.33406	−	0.427160i	0.403116	−	0.0234788i	0.258506	+	0.966010i	$0.416770\pi$
$332$	−14.6822	+	30.1316i	−0.805792	+	1.65369i
$333$	−17.3663	−	12.4193i	−0.951666	−	0.680572i
$334$	0.509610	−	0.958869i	0.0278846	−	0.0524670i
$335$	12.7865	−	17.1752i	0.698601	−	0.938383i
$336$	−1.55518	+	1.66333i	−0.0848422	+	0.0907420i
$337$	−1.46669	+	1.55460i	−0.0798958	+	0.0846846i	−0.766088	−	0.642736i	$-0.777799\pi$
$337$	−1.46669	+	1.55460i	−0.0798958	+	0.0846846i	0.686192	+	0.727420i	$0.259281\pi$
$338$	−0.393803	+	17.0564i	−0.0214200	+	0.927744i
$339$	−26.4885	−	10.2308i	−1.43866	−	0.555662i
$340$	−5.16265	−	4.75483i	−0.279984	−	0.257867i
$341$	3.12994	+	0.551893i	0.169496	+	0.0298867i
$342$	−1.21888	−	1.46429i	−0.0659095	−	0.0791799i
$343$	−4.49656	+	0.792864i	−0.242791	+	0.0428106i
$344$	9.10432	−	24.1774i	0.490872	−	1.30356i
$345$	−4.40860	−	6.16961i	−0.237351	−	0.332161i
$346$	3.46853	+	3.04961i	0.186469	+	0.163948i
$347$	−0.352348	+	6.04958i	−0.0189150	+	0.324758i	0.975556	+	0.219750i	$0.0705241\pi$
$347$	−0.352348	+	6.04958i	−0.0189150	+	0.324758i	−0.994471	+	0.105009i	$0.966513\pi$
$348$	5.58108	+	2.45731i	0.299177	+	0.131726i
$349$	−5.53863	−	5.87061i	−0.296476	−	0.314246i	0.561962	−	0.827163i	$-0.310047\pi$
$349$	−5.53863	−	5.87061i	−0.296476	−	0.314246i	−0.858439	+	0.512916i	$0.828565\pi$
$350$	−0.856177	−	0.950524i	−0.0457646	−	0.0508076i
$351$	−3.00369	+	4.03148i	−0.160325	+	0.215184i
$352$	−3.10716	+	1.79779i	−0.165612	+	0.0958225i
$353$	−4.58530	−	19.3469i	−0.244051	−	1.02973i	−0.947695	−	0.319179i	$-0.896593\pi$
$353$	−4.58530	−	19.3469i	−0.244051	−	1.02973i	0.703644	−	0.710553i	$-0.251555\pi$
$354$	−14.7380	+	1.08894i	−0.783315	+	0.0578765i
$355$	−0.643756	−	1.28182i	−0.0341670	−	0.0680322i
$356$	−7.20591	−	12.1419i	−0.381913	−	0.643519i
$357$	0.753816	−	1.09879i	0.0398962	−	0.0581544i
$358$	3.94109	−	15.0697i	0.208293	−	0.796460i
$359$	20.7454	+	7.55071i	1.09490	+	0.398511i	0.825434	−	0.564499i	$-0.190930\pi$
$359$	20.7454	+	7.55071i	1.09490	+	0.398511i	0.269466	+	0.963010i	$0.413153\pi$
$360$	0.637239	−	12.7057i	0.0335854	−	0.669648i
$361$	−17.6647	+	6.42941i	−0.929719	+	0.338390i
$362$	−0.184374	−	1.97102i	−0.00969048	−	0.103594i
$363$	−18.0106	−	3.53951i	−0.945309	−	0.185776i
$364$	−0.482261	+	0.414635i	−0.0252773	+	0.0217328i
$365$	15.8992	−	4.75991i	0.832203	−	0.249145i
$366$	−0.183740	−	11.7962i	−0.00960425	−	0.616597i
$367$	3.18748	−	27.2706i	0.166385	−	1.42352i	−0.609572	−	0.792731i	$-0.708659\pi$
$367$	3.18748	−	27.2706i	0.166385	−	1.42352i	0.775957	−	0.630785i	$-0.217267\pi$
$368$	−4.36744	+	10.8331i	−0.227669	+	0.564714i
$369$	−1.34008	−	1.08144i	−0.0697620	−	0.0562975i
$370$	14.9429	+	2.09724i	0.776843	+	0.109030i
$371$	−2.55874	−	1.28505i	−0.132843	−	0.0667163i
$372$	17.0627	+	3.14090i	0.884658	+	0.162848i
$373$	−10.0232	+	1.17154i	−0.518979	+	0.0606600i	−0.371550	−	0.928413i	$-0.621174\pi$
$373$	−10.0232	+	1.17154i	−0.518979	+	0.0606600i	−0.147429	+	0.989073i	$0.547100\pi$
$374$	1.63993	−	1.31277i	0.0847986	−	0.0678815i
$375$	19.9454	+	2.72686i	1.02998	+	0.140814i
$376$	7.19087	+	6.17085i	0.370841	+	0.318237i
$377$	1.47502	+	0.851604i	0.0759675	+	0.0438598i
$378$	2.40483	−	0.224038i	0.123691	−	0.0115233i
$379$	11.9497	−	6.89918i	0.613817	−	0.354387i	−0.160641	−	0.987013i	$-0.551356\pi$
$379$	11.9497	−	6.89918i	0.613817	−	0.354387i	0.774458	+	0.632626i	$0.218023\pi$
$380$	1.24271	+	0.518444i	0.0637499	+	0.0265956i
$381$	4.26229	+	4.69818i	0.218364	+	0.240695i
$382$	−28.0016	+	4.27353i	−1.43269	+	0.218653i
$383$	8.20335	+	11.0190i	0.419171	+	0.563045i	0.960683	−	0.277649i	$-0.0895551\pi$
$383$	8.20335	+	11.0190i	0.419171	+	0.563045i	−0.541511	+	0.840693i	$0.682148\pi$
$384$	−17.0346	+	9.68617i	−0.869294	+	0.494295i
$385$	−0.261260	+	0.171834i	−0.0133151	+	0.00875745i
$386$	−10.5909	+	4.28130i	−0.539063	+	0.217913i
$387$	−24.2474	+	12.7644i	−1.23256	+	0.648849i
$388$	5.02737	+	20.1316i	0.255226	+	1.02203i
$389$	−18.9073	+	8.15582i	−0.958638	+	0.413516i	−0.817151	−	0.576424i	$-0.804448\pi$
$389$	−18.9073	+	8.15582i	−0.958638	+	0.413516i	−0.141487	+	0.989940i	$0.545188\pi$
$390$	0.562429	−	3.50837i	0.0284797	−	0.177653i
$391$	1.57627	−	6.65081i	0.0797155	−	0.336346i
$392$	−19.3354	−	2.47734i	−0.976585	−	0.125124i
$393$	0.547883	−	28.0664i	0.0276370	−	1.41576i
$394$	11.5637	−	25.1923i	0.582571	−	1.26917i
$395$	−13.5363	−	11.3583i	−0.681087	−	0.571500i
$396$	3.73045	+	0.762262i	0.187462	+	0.0383051i
$397$	23.7055	−	19.8912i	1.18974	−	0.998313i	0.189879	−	0.981808i	$-0.439190\pi$
$397$	23.7055	−	19.8912i	1.18974	−	0.998313i	0.999864	−	0.0165050i	$-0.00525396\pi$
$398$	6.99625	+	25.4970i	0.350690	+	1.27805i
$399$	−0.0637987	+	0.247553i	−0.00319393	+	0.0123931i
$400$	−4.60190	−	10.0009i	−0.230095	−	0.500045i
$401$	−10.5338	+	16.0159i	−0.526035	+	0.799797i	−0.996585	−	0.0825766i	$-0.973685\pi$
$401$	−10.5338	+	16.0159i	−0.526035	+	0.799797i	0.470550	+	0.882373i	$0.344055\pi$
$402$	24.4004	+	25.0689i	1.21698	+	1.25032i
$403$	4.64212	+	1.38976i	0.231241	+	0.0692289i
$404$	9.97682	+	22.3858i	0.496366	+	1.11374i
$405$	−9.45312	+	9.62854i	−0.469729	+	0.478446i
$406$	−0.170272	−	0.800333i	−0.00845048	−	0.0397199i
$407$	−1.29525	+	4.32644i	−0.0642033	+	0.214454i
$408$	9.00562	−	7.09873i	0.445845	−	0.351439i
$409$	−4.30992	−	2.83468i	−0.213112	−	0.140166i	0.438466	−	0.898748i	$-0.355522\pi$
$409$	−4.30992	−	2.83468i	−0.213112	−	0.140166i	−0.651577	+	0.758582i	$0.725892\pi$
$410$	1.19336	+	0.238947i	0.0589359	+	0.0118008i
$411$	−2.48354	−	8.92611i	−0.122504	−	0.440293i
$412$	−22.7292	+	11.7589i	−1.11979	+	0.579322i
$413$	1.27461	+	1.51902i	0.0627194	+	0.0747461i
$414$	11.0929	−	5.51642i	0.545189	−	0.271117i
$415$	−16.1509	+	19.2479i	−0.792817	+	0.944843i
$416$	−5.02352	+	2.17250i	−0.246298	+	0.106516i
$417$	3.28465	−	5.44109i	0.160850	−	0.266452i
$418$	−0.209506	+	0.344271i	−0.0102473	+	0.0168388i
$419$	17.6720	+	4.18835i	0.863335	+	0.204614i	0.638348	−	0.769748i	$-0.279618\pi$
$419$	17.6720	+	4.18835i	0.863335	+	0.204614i	0.224987	+	0.974362i	$0.427766\pi$
$420$	−1.43318	+	0.927273i	−0.0699318	+	0.0452463i
$421$	5.85023	+	13.5624i	0.285123	+	0.660989i	0.999238	−	0.0390395i	$-0.0124298\pi$
$421$	5.85023	+	13.5624i	0.285123	+	0.660989i	−0.714115	+	0.700029i	$0.753171\pi$
$422$	1.06403	+	30.3073i	0.0517959	+	1.47534i
$423$	−1.35763	−	9.95833i	−0.0660103	−	0.484191i
$424$	−17.7344	−	17.1067i	−0.861258	−	0.830775i
$425$	3.54001	+	5.38232i	0.171716	+	0.261081i
$426$	2.23432	−	0.707012i	0.108253	−	0.0342549i
$427$	−1.26977	+	0.945307i	−0.0614484	+	0.0457466i
$428$	8.20511	+	21.7279i	0.396609	+	1.05026i
$429$	1.01262	+	0.324826i	0.0488900	+	0.0156827i
$430$	11.0127	−	15.9305i	0.531080	−	0.768238i
$431$	−1.20028	−	2.07895i	−0.0578154	−	0.100139i	0.835669	−	0.549233i	$-0.185080\pi$
$431$	−1.20028	−	2.07895i	−0.0578154	−	0.100139i	−0.893485	+	0.449094i	$0.851747\pi$
$432$	20.3320	+	4.31385i	0.978224	+	0.207550i
$433$	−1.16773	+	2.02256i	−0.0561174	+	0.0971981i	−0.892719	−	0.450613i	$-0.851205\pi$
$433$	−1.16773	+	2.02256i	−0.0561174	+	0.0971981i	0.836602	+	0.547811i	$0.184539\pi$
$434$	−0.996481	−	2.10389i	−0.0478326	−	0.100990i
$435$	3.61279	+	2.80085i	0.173220	+	0.134290i
$436$	20.6545	−	25.2241i	0.989170	−	1.20802i
$437$	0.152233	+	1.30243i	0.00728228	+	0.0623039i
$438$	3.56695	+	26.8796i	0.170436	+	1.28436i
$439$	−12.6811	+	25.2501i	−0.605235	+	1.20512i	0.357306	+	0.933987i	$0.383695\pi$
$439$	−12.6811	+	25.2501i	−0.605235	+	1.20512i	−0.962541	+	0.271135i	$0.912601\pi$
$440$	−2.58634	+	0.743190i	−0.123299	+	0.0354302i
$441$	13.5909	+	15.5814i	0.647187	+	0.741972i
$442$	2.71578	−	1.69771i	0.129176	−	0.0807519i
$443$	34.1683	+	3.99370i	1.62339	+	0.189747i	0.878600	−	0.477558i	$-0.158478\pi$
$443$	34.1683	+	3.99370i	1.62339	+	0.189747i	0.744785	+	0.667304i	$0.232552\pi$
$444$	−7.24769	+	23.5635i	−0.343960	+	1.11827i
$445$	−3.03557	−	10.1395i	−0.143900	−	0.480659i
$446$	16.9759	+	31.0362i	0.803831	+	1.46960i
$447$	−14.5412	+	4.97338i	−0.687777	+	0.235233i
$448$	2.39069	+	1.09466i	0.112949	+	0.0517180i
$449$	1.03039	+	2.83098i	0.0486272	+	0.133602i	0.961629	−	0.274354i	$-0.0884639\pi$
$449$	1.03039	+	2.83098i	0.0486272	+	0.133602i	−0.913002	+	0.407956i	$0.866242\pi$
$450$	−3.39300	+	11.1728i	−0.159947	+	0.526693i
$451$	−0.124583	+	0.342289i	−0.00586639	+	0.0161178i
$452$	−1.51325	+	32.7535i	−0.0711775	+	1.54060i
$453$	14.7380	−	7.04495i	0.692454	−	0.331001i
$454$	−2.68359	−	7.93865i	−0.125947	−	0.372579i
$455$	−0.426053	+	0.213972i	−0.0199737	+	0.0100312i
$456$	−1.15774	+	1.87067i	−0.0542160	+	0.0876022i
$457$	34.9927	−	8.29343i	1.63689	−	0.387950i	0.693716	−	0.720249i	$-0.255972\pi$
$457$	34.9927	−	8.29343i	1.63689	−	0.387950i	0.943174	+	0.332299i	$0.107824\pi$
$458$	−1.94871	−	0.632773i	−0.0910575	−	0.0295676i
$459$	−12.1418	−	0.711782i	−0.566731	−	0.0332231i
$460$	−5.14396	+	7.08562i	−0.239839	+	0.330369i
$461$	−10.8823	+	10.2669i	−0.506840	+	0.478179i	−0.896665	−	0.442710i	$-0.854017\pi$
$461$	−10.8823	+	10.2669i	−0.506840	+	0.478179i	0.389825	+	0.920889i	$0.372536\pi$
$462$	−0.209637	−	0.465904i	−0.00975320	−	0.0216758i
$463$	11.1874	+	0.651589i	0.519920	+	0.0302819i	0.316099	−	0.948726i	$-0.397627\pi$
$463$	11.1874	+	0.651589i	0.519920	+	0.0302819i	0.203821	+	0.979008i	$0.434664\pi$
$464$	0.649265	−	7.01149i	0.0301414	−	0.325500i
$465$	11.8391	+	5.38334i	0.549026	+	0.249647i
$466$	10.8793	−	11.0107i	0.503973	−	0.510062i
$467$	6.43692	+	36.5056i	0.297865	+	1.68928i	0.655324	+	0.755348i	$0.272532\pi$
$467$	6.43692	+	36.5056i	0.297865	+	1.68928i	−0.357458	+	0.933929i	$0.616357\pi$
$468$	5.51426	+	1.81462i	0.254897	+	0.0838810i
$469$	0.815116	−	4.62275i	0.0376386	−	0.213459i
$470$	4.10911	+	5.79406i	0.189539	+	0.267260i
$471$	−0.787736	−	0.976891i	−0.0362970	−	0.0450128i
$472$	6.58490	+	15.7427i	0.303095	+	0.724615i
$473$	4.21608	+	3.97767i	0.193856	+	0.182893i
$474$	21.8240	−	18.8994i	1.00241	−	0.868079i
$475$	−0.991358	−	0.738039i	−0.0454866	−	0.0338636i
$476$	−1.47921	−	0.423557i	−0.0677993	−	0.0194137i
$477$	2.01871	+	26.0570i	0.0924302	+	1.19307i
$478$	−33.4892	−	26.1545i	−1.53176	−	1.19628i
$479$	−1.42756	−	24.5103i	−0.0652271	−	1.11991i	−0.859095	−	0.511816i	$-0.828973\pi$
$479$	−1.42756	−	24.5103i	−0.0652271	−	1.11991i	0.793868	−	0.608090i	$-0.208064\pi$
$480$	−14.1484	+	3.95081i	−0.645784	+	0.180329i
$481$	−2.72725	+	6.32246i	−0.124352	+	0.288280i
$482$	−9.60986	+	24.6193i	−0.437717	+	1.12138i
$483$	−1.47068	−	0.774910i	−0.0669183	−	0.0352596i
$484$	2.71317	+	21.0202i	0.123326	+	0.955464i
$485$			15.5547i			0.706303i
$486$	−13.0881	−	17.7399i	−0.593687	−	0.804696i
$487$		−	32.8889i		−	1.49034i	−0.666875	−	0.745170i	$-0.732368\pi$
$487$		−	32.8889i		−	1.49034i	0.666875	−	0.745170i	$-0.267632\pi$
$488$	−12.8520	+	4.51719i	−0.581782	+	0.204483i
$489$	9.64308	+	5.08099i	0.436075	+	0.229770i
$490$	−13.6126	−	5.31352i	−0.614954	−	0.240040i
$491$	−0.865048	+	2.00541i	−0.0390391	+	0.0905027i	−0.936620	−	0.350347i	$-0.886064\pi$
$491$	−0.865048	+	2.00541i	−0.0390391	+	0.0905027i	0.897581	+	0.440850i	$0.145323\pi$
$492$	−0.694089	+	1.86334i	−0.0312919	+	0.0840057i
$493$	0.239586	+	4.11353i	0.0107904	+	0.185264i
$494$	−0.378201	+	0.484262i	−0.0170161	+	0.0217880i
$495$	2.57469	+	1.23193i	0.115724	+	0.0553710i
$496$	−2.80292	−	19.8362i	−0.125855	−	0.890674i
$497$	−0.252231	−	0.187779i	−0.0113141	−	0.00842303i
$498$	−26.8739	−	31.0324i	−1.20425	−	1.39060i
$499$	−11.9307	−	11.2560i	−0.534092	−	0.503890i	0.371273	−	0.928524i	$-0.378921\pi$
$499$	−11.9307	−	11.2560i	−0.534092	−	0.503890i	−0.905365	+	0.424634i	$0.860403\pi$
$500$	−4.31110	−	22.8419i	−0.192798	−	1.02152i
$501$	0.834812	+	1.03527i	0.0372967	+	0.0462525i
$502$	−17.2736	+	12.2503i	−0.770959	+	0.546759i
$503$	5.21046	−	29.5500i	0.232323	−	1.31757i	−0.615856	−	0.787859i	$-0.711190\pi$
$503$	5.21046	−	29.5500i	0.232323	−	1.31757i	0.848179	−	0.529710i	$-0.177699\pi$
$504$	−1.12524	−	2.55181i	−0.0501222	−	0.113667i
$505$	3.19030	+	18.0931i	0.141967	+	0.805133i
$506$	−1.86415	−	1.84189i	−0.0828714	−	0.0818821i
$507$	−19.0212	−	8.64908i	−0.844761	−	0.384119i
$508$	3.58598	−	6.38702i	0.159102	−	0.283378i
$509$	36.7091	+	2.13806i	1.62710	+	0.0947680i	0.847250	−	0.531194i	$-0.178256\pi$
$509$	36.7091	+	2.13806i	1.62710	+	0.0947680i	0.779854	+	0.625962i	$0.215293\pi$
$510$	7.83904	−	3.52723i	0.347119	−	0.156189i
$511$	2.64643	−	2.49678i	0.117071	−	0.110451i
$512$	16.8409	+	15.1124i	0.744269	+	0.667880i
$513$	2.23562	−	0.668381i	0.0987051	−	0.0295097i
$514$	−7.03572	+	21.6675i	−0.310333	+	0.955713i
$515$	−18.6666	+	4.42406i	−0.822547	+	0.194947i
$516$	22.8511	+	21.8856i	1.00596	+	0.963458i
$517$	−1.89983	+	0.954131i	−0.0835545	+	0.0419627i
$518$	3.13373	−	1.05933i	0.137688	−	0.0465443i
$519$	−5.10344	+	2.43950i	−0.224016	+	0.107082i
$520$	−4.04816	+	0.667660i	−0.177523	+	0.0292788i
$521$	−6.96138	+	19.1262i	−0.304984	+	0.837936i	0.688631	+	0.725112i	$0.258212\pi$
$521$	−6.96138	+	19.1262i	−0.304984	+	0.837936i	−0.993615	+	0.112824i	$0.964010\pi$
$522$	−5.45265	+	5.10382i	−0.238656	+	0.223388i
$523$	4.11353	+	11.3018i	0.179872	+	0.494195i	0.996559	−	0.0828864i	$-0.0264139\pi$
$523$	4.11353	+	11.3018i	0.179872	+	0.494195i	−0.816687	+	0.577081i	$0.804192\pi$
$524$	−30.9388	+	9.66881i	−1.35157	+	0.422384i
$525$	1.48247	−	0.507033i	0.0647003	−	0.0221288i
$526$	29.8322	−	16.3174i	1.30075	−	0.711471i
$527$	3.36219	+	11.2305i	0.146459	+	0.489209i
$528$	−0.530055	−	4.36449i	−0.0230677	−	0.189940i
$529$	14.3752	+	1.68022i	0.625010	+	0.0730532i
$530$	−9.79115	−	15.6626i	−0.425300	−	0.680340i
$531$	5.86373	−	17.1233i	0.254464	−	0.743089i
$532$	0.294463	−	0.0207014i	0.0127666	−	0.000897521i
$533$	−0.249248	+	0.496293i	−0.0107961	+	0.0214968i
$534$	17.1421	−	2.27477i	0.741811	−	0.0984391i
$535$	2.02124	+	17.2928i	0.0873858	+	0.747633i
$536$	18.5280	−	35.8955i	0.800288	−	1.55045i
$537$	15.0771	+	11.6887i	0.650624	+	0.504403i
$538$	25.9984	−	12.3138i	1.12087	−	0.530888i
$539$	2.18678	−	3.78762i	0.0941914	−	0.163144i
$540$	14.0039	+	6.83021i	0.602631	+	0.293926i
$541$	14.6879	+	25.4402i	0.631483	+	1.09376i	0.987249	+	0.159186i	$0.0508869\pi$
$541$	14.6879	+	25.4402i	0.631483	+	1.09376i	−0.355765	+	0.934575i	$0.615780\pi$
$542$	−7.92626	−	5.47939i	−0.340462	−	0.235360i
$543$	2.30866	+	0.740564i	0.0990742	+	0.0317806i
$544$	−11.0695	−	7.26571i	−0.474601	−	0.311515i
$545$	19.6032	−	14.5940i	0.839708	−	0.625140i
$546$	−0.234997	−	0.742646i	−0.0100569	−	0.0317823i
$547$	12.2043	+	18.5557i	0.521817	+	0.793384i	0.996215	−	0.0869266i	$-0.0277046\pi$
$547$	12.2043	+	18.5557i	0.521817	+	0.793384i	−0.474398	+	0.880311i	$0.657334\pi$
$548$	−8.86722	+	5.98584i	−0.378789	+	0.255702i
$549$	13.3745	+	5.46801i	0.570809	+	0.233369i
$550$	2.46844	−	0.0866616i	0.105255	−	0.00369527i
$551$	−0.313107	−	0.725865i	−0.0133388	−	0.0309229i
$552$	−10.1002	−	10.1307i	−0.429895	−	0.431191i
$553$	−3.76936	−	0.893355i	−0.160289	−	0.0379893i
$554$	−10.7236	−	6.52583i	−0.455600	−	0.277256i
$555$	−9.55090	+	15.8213i	−0.405413	+	0.671575i
$556$	−7.16088	−	1.60659i	−0.303689	−	0.0681344i
$557$	15.7526	−	18.7732i	0.667458	−	0.795446i	−0.320977	−	0.947087i	$-0.604011\pi$
$557$	15.7526	−	18.7732i	0.667458	−	0.795446i	0.988436	+	0.151641i	$0.0484558\pi$
$558$	−11.7462	+	17.7067i	−0.497255	+	0.749584i
$559$	5.68055	+	6.76981i	0.240261	+	0.286332i
$560$	1.53992	+	1.23035i	0.0650734	+	0.0519918i
$561$	0.689631	+	2.47861i	0.0291162	+	0.104647i
$562$	−0.764635	+	3.81878i	−0.0322542	+	0.161085i
$563$	−11.5652	−	7.60652i	−0.487413	−	0.320577i	0.281905	−	0.959442i	$-0.409034\pi$
$563$	−11.5652	−	7.60652i	−0.487413	−	0.320577i	−0.769318	+	0.638866i	$0.779404\pi$
$564$	−10.4097	+	5.13041i	−0.438326	+	0.216029i
$565$	−7.04940	+	23.5466i	−0.296570	+	0.990614i
$566$	15.9997	−	3.40396i	0.672516	−	0.143079i
$567$	−0.904591	+	2.81635i	−0.0379893	+	0.118276i
$568$	−1.59181	−	2.18836i	−0.0667908	−	0.0918214i
$569$	4.87625	+	1.45985i	0.204423	+	0.0612002i	0.387378	−	0.921921i	$-0.373381\pi$
$569$	4.87625	+	1.45985i	0.204423	+	0.0612002i	−0.182955	+	0.983121i	$0.558566\pi$
$570$	−1.18177	+	1.15026i	−0.0494991	+	0.0481790i
$571$	18.1809	−	27.6428i	0.760848	−	1.15681i	−0.222474	−	0.974939i	$-0.571413\pi$
$571$	18.1809	−	27.6428i	0.760848	−	1.15681i	0.983322	−	0.181875i	$-0.0582165\pi$
$572$	−0.0147465	−	1.22787i	−0.000616584	−	0.0513400i
$573$	8.65781	−	33.5942i	0.361685	−	1.40342i
$574$	0.257295	−	0.0706006i	0.0107393	−	0.00294681i
$575$	6.15649	−	5.16590i	0.256743	−	0.215433i
$576$	−2.71448	−	23.8460i	−0.113103	−	0.993583i
$577$	3.82174	+	3.20682i	0.159101	+	0.133502i	0.718863	−	0.695152i	$-0.244663\pi$
$577$	3.82174	+	3.20682i	0.159101	+	0.133502i	−0.559762	+	0.828654i	$0.689107\pi$
$578$	−14.8078	−	6.79706i	−0.615925	−	0.282720i
$579$	0.273064	−	13.9882i	0.0113481	−	0.581331i
$580$	1.74566	−	4.98150i	0.0724846	−	0.206845i
$581$	−1.27030	+	5.35982i	−0.0527009	+	0.222363i
$582$	−25.0929	−	4.02265i	−1.04013	−	0.166744i
$583$	5.07621	−	2.18966i	0.210235	−	0.0906865i
$584$	28.1335	−	13.7412i	1.16417	−	0.568614i
$585$	3.68092	+	2.32129i	0.152187	+	0.0959734i
$586$	−10.0029	−	24.7448i	−0.413216	−	1.02220i
$587$	−18.0594	+	11.8779i	−0.745393	+	0.490253i	−0.864503	−	0.502628i	$-0.832366\pi$
$587$	−18.0594	+	11.8779i	−0.745393	+	0.490253i	0.119109	+	0.992881i	$0.461996\pi$
$588$	12.0922	−	20.5857i	0.498673	−	0.848940i
$589$	−1.34304	−	1.80401i	−0.0553390	−	0.0743331i
$590$	1.92993	+	12.6455i	0.0794539	+	0.520608i
$591$	22.8110	+	25.1438i	0.938321	+	1.03428i
$592$	28.4586	−	0.683662i	1.16964	−	0.0280983i
$593$	−11.8774	+	6.85743i	−0.487747	+	0.281601i	−0.723639	−	0.690178i	$-0.757532\pi$
$593$	−11.8774	+	6.85743i	−0.487747	+	0.281601i	0.235892	+	0.971779i	$0.424199\pi$
$594$	−2.65320	+	3.83490i	−0.108862	+	0.157348i
$595$	−0.998891	−	0.576710i	−0.0409505	−	0.0236428i
$596$	10.7672	+	14.1059i	0.441040	+	0.577802i
$597$	−32.0831	−	4.38627i	−1.31307	−	0.179518i
$598$	−2.49694	−	3.11922i	−0.102108	−	0.127554i
$599$	5.77325	−	0.674796i	0.235889	−	0.0275714i	0.00267285	−	0.999996i	$-0.499149\pi$
$599$	5.77325	−	0.674796i	0.235889	−	0.0275714i	0.233216	+	0.972425i	$0.425075\pi$
$600$	13.4779	−	0.371872i	0.550235	−	0.0151816i
$601$	2.38712	+	1.19886i	0.0973725	+	0.0489023i	0.496819	−	0.867854i	$-0.334501\pi$
$601$	2.38712	+	1.19886i	0.0973725	+	0.0489023i	−0.399446	+	0.916757i	$0.630798\pi$
$602$	0.590087	−	4.20439i	0.0240502	−	0.171358i
$603$	−39.9738	+	15.4220i	−1.62786	+	0.628031i
$604$	−13.1080	−	13.5635i	−0.533355	−	0.551893i
$605$	−1.84450	+	15.7807i	−0.0749894	+	0.641576i
$606$	−30.0129	+	0.467487i	−1.21919	+	0.0189904i
$607$	−19.9364	+	5.96855i	−0.809192	+	0.242256i	−0.664565	−	0.747230i	$-0.731383\pi$
$607$	−19.9364	+	5.96855i	−0.809192	+	0.242256i	−0.144626	+	0.989486i	$0.546198\pi$
$608$	2.47235	+	0.583519i	0.100267	+	0.0236648i
$609$	0.983333	+	0.193249i	0.0398467	+	0.00783084i
$610$	−10.1676	+	0.951103i	−0.411674	+	0.0385090i
$611$	−3.04588	+	1.10861i	−0.123223	+	0.0448496i
$612$	3.66286	+	13.5581i	0.148062	+	0.548055i
$613$	−20.9633	−	7.63001i	−0.846699	−	0.308173i	−0.118005	−	0.993013i	$-0.537650\pi$
$613$	−20.9633	−	7.63001i	−0.846699	−	0.308173i	−0.728694	+	0.684840i	$0.759872\pi$
$614$	14.2968	+	3.73895i	0.576971	+	0.150892i
$615$	−0.843233	+	1.22913i	−0.0340024	+	0.0495634i
$616$	−0.433558	+	0.400059i	−0.0174685	+	0.0161188i
$617$	−9.91103	−	19.7345i	−0.399003	−	0.794480i	0.600986	−	0.799260i	$-0.294775\pi$
$617$	−9.91103	−	19.7345i	−0.399003	−	0.794480i	−0.999989	+	0.00477968i	$0.998479\pi$
$618$	−2.30948	−	31.2570i	−0.0929008	−	1.25734i
$619$	5.69927	+	24.0471i	0.229073	+	0.966535i	0.959089	+	0.283105i	$0.0913645\pi$
$619$	5.69927	+	24.0471i	0.229073	+	0.966535i	−0.730016	+	0.683430i	$0.760487\pi$
$620$	1.56418	−	14.9359i	0.0628190	−	0.599839i
$621$	0.876522	+	15.1479i	0.0351736	+	0.607863i
$622$	29.1238	−	26.2331i	1.16776	−	1.05185i
$623$	−1.59228	−	1.68772i	−0.0637935	−	0.0676172i
$624$	−0.0301643	−	6.70316i	−0.00120754	−	0.268341i
$625$	0.213053	−	3.65799i	0.00852214	−	0.146319i
$626$	14.8619	−	16.9035i	0.594002	−	0.675600i
$627$	−0.286963	−	0.401591i	−0.0114602	−	0.0160380i
$628$	−0.781678	+	1.22015i	−0.0311924	+	0.0486894i
$629$	−16.4050	+	2.89264i	−0.654109	+	0.115337i
$630$	−0.354913	−	2.06029i	−0.0141401	−	0.0820838i
$631$	−3.25658	−	0.574222i	−0.129642	−	0.0228594i	0.108450	−	0.994102i	$-0.465411\pi$
$631$	−3.25658	−	0.574222i	−0.129642	−	0.0228594i	−0.238093	+	0.971242i	$0.576522\pi$
$632$	−28.6836	−	16.9868i	−1.14097	−	0.675697i
$633$	−34.6471	−	13.3819i	−1.37710	−	0.531885i
$634$	−28.4804	−	0.657564i	−1.13110	−	0.0261152i
$635$	3.76810	−	3.99395i	0.149532	−	0.158495i
$636$	27.7991	−	11.7445i	1.10230	−	0.465702i
$637$	3.98196	−	5.34870i	0.157771	−	0.211923i
$638$	1.39505	+	0.741426i	0.0552305	+	0.0293533i
$639$	−0.278587	+	2.85666i	−0.0110207	+	0.113008i
$640$	9.50352	+	14.0499i	0.375660	+	0.555370i
$641$	−7.83940	+	0.456593i	−0.309638	+	0.0180343i	−0.212260	−	0.977213i	$-0.568082\pi$
$641$	−7.83940	+	0.456593i	−0.309638	+	0.0180343i	−0.0973775	+	0.995248i	$0.531045\pi$
$642$	−28.4195	−	1.21148i	−1.12163	−	0.0478133i
$643$	29.8781	+	12.8882i	1.17828	+	0.508260i	0.892944	−	0.450168i	$-0.148636\pi$
$643$	29.8781	+	12.8882i	1.17828	+	0.508260i	0.285335	+	0.958428i	$0.407895\pi$
$644$	−0.310594	+	1.89421i	−0.0122391	+	0.0746425i
$645$	12.6446	+	20.0676i	0.497879	+	0.790159i
$646$	−1.48160	−	0.120664i	−0.0582929	−	0.00474744i
$647$	−25.0999			−0.986778			−0.493389	−	0.869809i	$-0.664242\pi$
$647$	−25.0999			−0.986778			−0.493389	+	0.869809i	$0.664242\pi$
$648$	−14.6401	+	20.8247i	−0.575117	+	0.818071i
$649$	−3.82857			−0.150285
$650$	3.75341	+	0.305682i	0.147221	+	0.0119898i
$651$	2.84900	−	0.110195i	0.111661	−	0.00431888i
$652$	2.03653	−	12.4201i	0.0797567	−	0.486410i
$653$	−6.33668	−	2.73338i	−0.247974	−	0.106965i	0.268465	−	0.963289i	$-0.413483\pi$
$653$	−6.33668	−	2.73338i	−0.247974	−	0.106965i	−0.516439	+	0.856324i	$0.672743\pi$
$654$	18.4735	+	35.3981i	0.722370	+	1.38418i
$655$	−24.2577	+	1.41285i	−0.947828	+	0.0552047i
$656$	2.29468	+	0.0784149i	0.0895922	+	0.00306159i
$657$	−31.9906	−	8.91387i	−1.24807	−	0.347763i
$658$	1.37506	+	0.730803i	0.0536054	+	0.0284897i
$659$	8.28084	−	11.1231i	0.322576	−	0.433295i	−0.611024	−	0.791612i	$-0.709242\pi$
$659$	8.28084	−	11.1231i	0.322576	−	0.433295i	0.933600	+	0.358318i	$0.116649\pi$
$660$	0.407188	−	3.27054i	0.0158498	−	0.127306i
$661$	−2.14894	+	2.27775i	−0.0835842	+	0.0885941i	−0.767816	−	0.640671i	$-0.778656\pi$
$661$	−2.14894	+	2.27775i	−0.0835842	+	0.0885941i	0.684231	+	0.729265i	$0.260138\pi$
$662$	10.3867	+	0.239812i	0.403692	+	0.00932056i
$663$	0.605622	+	3.87553i	0.0235204	+	0.150513i
$664$	−24.1542	+	40.7864i	−0.937366	+	1.58282i
$665$	0.217921	+	0.0384254i	0.00845062	+	0.00149007i
$666$	−23.0529	−	19.4991i	−0.893282	−	0.755575i
$667$	5.06234	−	0.892627i	0.196015	−	0.0345627i
$668$	0.828392	−	1.29307i	0.0320515	−	0.0500304i
$669$	−43.1229	+	4.18899i	−1.66723	+	0.161956i
$670$	19.9948	−	22.7415i	0.772466	−	0.878580i
$671$	0.177714	−	3.05123i	0.00686058	−	0.117792i
$672$	−2.38304	+	2.16601i	−0.0919279	+	0.0835558i
$673$	0.686894	+	0.728066i	0.0264778	+	0.0280649i	0.740477	−	0.672081i	$-0.234600\pi$
$673$	0.686894	+	0.728066i	0.0264778	+	0.0280649i	−0.713999	+	0.700146i	$0.753118\pi$
$674$	−2.24583	+	2.02292i	−0.0865062	+	0.0779198i
$675$	−10.9517	−	9.19661i	−0.421531	−	0.353978i
$676$	−2.51307	+	23.9965i	−0.0966566	+	0.922944i
$677$	0.815570	+	3.44116i	0.0313449	+	0.132255i	0.986468	−	0.163955i	$-0.0524253\pi$
$677$	0.815570	+	3.44116i	0.0313449	+	0.132255i	−0.955123	+	0.296210i	$0.904277\pi$
$678$	−36.1624	−	17.4616i	−1.38881	−	0.670608i
$679$	1.53039	+	3.04725i	0.0587309	+	0.116943i
$680$	−6.73116	−	7.29480i	−0.258128	−	0.279743i
$681$	10.2324	+	0.796618i	0.392105	+	0.0305265i
$682$	4.34844	+	1.13722i	0.166510	+	0.0435464i
$683$	35.7375	+	13.0074i	1.36746	+	0.497714i	0.918352	−	0.395764i	$-0.129520\pi$
$683$	35.7375	+	13.0074i	1.36746	+	0.497714i	0.449106	+	0.893478i	$0.351742\pi$
$684$	−1.54997	−	2.20391i	−0.0592648	−	0.0842687i
$685$	−7.53626	+	2.74297i	−0.287946	+	0.104804i
$686$	−6.42912	+	0.601396i	−0.245465	+	0.0229614i
$687$	1.65019	−	1.89043i	0.0629586	−	0.0721243i
$688$	15.6084	−	33.0340i	0.595065	−	1.25941i
$689$	8.07470	−	2.41741i	0.307622	−	0.0920959i
$690$	−5.50588	−	9.20244i	−0.209605	−	0.350331i
$691$	3.34411	−	28.6107i	0.127216	−	1.08840i	−0.767275	−	0.641318i	$-0.778388\pi$
$691$	3.34411	−	28.6107i	0.127216	−	1.08840i	0.894491	−	0.447085i	$-0.147538\pi$
$692$	4.53898	+	4.69674i	0.172546	+	0.178543i
$693$	0.625602	−	0.0119759i	0.0237647	−	0.000454928i
$694$	−1.19111	+	8.48672i	−0.0452140	+	0.322151i
$695$	−4.91627	−	2.46905i	−0.186485	−	0.0936562i
$696$	7.58471	+	4.10438i	0.287498	+	0.155576i
$697$	−1.33449	+	0.155979i	−0.0505474	+	0.00590814i
$698$	−7.13304	−	8.91070i	−0.269990	−	0.337275i
$699$	7.16757	+	17.5505i	0.271102	+	0.663819i
$700$	−1.09771	−	1.43809i	−0.0414894	−	0.0543548i
$701$	7.64760	+	4.41535i	0.288846	+	0.166765i	0.637421	−	0.770515i	$-0.280001\pi$
$701$	7.64760	+	4.41535i	0.288846	+	0.166765i	−0.348575	+	0.937281i	$0.613334\pi$
$702$	−4.69664	+	5.33774i	−0.177263	+	0.201460i
$703$	2.76768	−	1.59792i	0.104385	−	0.0602666i
$704$	−4.58606	+	2.17738i	−0.172844	+	0.0820632i
$705$	−8.50269	+	1.84068i	−0.320230	+	0.0693240i
$706$	−4.24226	−	27.7967i	−0.159660	−	1.04614i
$707$	2.40513	+	3.23065i	0.0904543	+	0.121501i
$708$	−20.8989	−	0.156938i	−0.785429	−	0.00589808i
$709$	−3.61893	+	2.38021i	−0.135912	+	0.0893905i	−0.615644	−	0.788024i	$-0.711104\pi$
$709$	−3.61893	+	2.38021i	−0.135912	+	0.0893905i	0.479732	+	0.877415i	$0.340734\pi$
$710$	−0.760257	−	1.88069i	−0.0285320	−	0.0705811i
$711$	10.7873	+	33.6726i	0.404556	+	1.26282i
$712$	−8.76324	−	17.9418i	−0.328416	−	0.672396i
$713$	13.4287	−	5.79257i	0.502908	−	0.216933i
$714$	1.18868	−	1.46227i	0.0444851	−	0.0547240i
$715$	0.212286	−	0.895705i	0.00793905	−	0.0334975i
$716$	7.28508	−	20.7891i	0.272256	−	0.776924i
$717$	45.5690	−	25.1364i	1.70181	−	0.938737i
$718$	28.3748	+	13.0245i	1.05894	+	0.486072i
$719$	−20.2419	−	16.9850i	−0.754897	−	0.633433i	0.181896	−	0.983318i	$-0.441776\pi$
$719$	−20.2419	−	16.9850i	−0.754897	−	0.633433i	−0.936793	+	0.349884i	$0.886221\pi$
$720$	2.35677	−	17.8361i	0.0878316	−	0.664712i
$721$	−3.22161	+	2.70325i	−0.119979	+	0.100674i
$722$	−25.6372	+	7.03474i	−0.954119	+	0.261806i
$723$	−23.1056	−	22.6676i	−0.859308	−	0.843015i
$724$	−0.0336203	−	2.79941i	−0.00124949	−	0.104039i
$725$	−2.66233	+	4.04788i	−0.0988765	+	0.150334i
$726$	−24.9804	−	7.05663i	−0.927109	−	0.261896i
$727$	−36.7704	−	11.0083i	−1.36374	−	0.408277i	−0.480416	−	0.877041i	$-0.659514\pi$
$727$	−36.7704	−	11.0083i	−1.36374	−	0.408277i	−0.883324	+	0.468764i	$0.844700\pi$
$728$	−0.727367	+	0.529086i	−0.0269580	+	0.0196092i
$729$	26.2769	−	6.20678i	0.973219	−	0.229881i
$730$	22.9571	−	4.88417i	0.849681	−	0.180771i
$731$	−6.13182	+	20.4817i	−0.226794	+	0.757543i
$732$	1.09516	−	16.6484i	0.0404781	−	0.615341i
$733$	6.60252	+	4.34254i	0.243870	+	0.160396i	0.665560	−	0.746344i	$-0.268193\pi$
$733$	6.60252	+	4.34254i	0.243870	+	0.160396i	−0.421691	+	0.906740i	$0.638563\pi$
$734$	7.62344	−	38.0733i	0.281386	−	1.40531i
$735$	12.5334	−	12.7756i	0.462302	−	0.471237i
$736$	−7.39970	+	14.7684i	−0.272756	+	0.544370i
$737$	5.82565	+	6.94274i	0.214591	+	0.255739i
$738$	−1.76477	−	1.67817i	−0.0649620	−	0.0617745i
$739$	−5.75894	+	6.86324i	−0.211846	+	0.252468i	−0.861495	−	0.507766i	$-0.830471\pi$
$739$	−5.75894	+	6.86324i	−0.211846	+	0.252468i	0.649649	+	0.760234i	$0.274916\pi$
$740$	20.8219	+	4.67152i	0.765429	+	0.171729i
$741$	−0.363479	−	0.658940i	−0.0133527	−	0.0242068i
$742$	−3.45914	−	2.10506i	−0.126989	−	0.0772793i
$743$	19.7898	+	4.69027i	0.726018	+	0.172069i	0.576975	−	0.816762i	$-0.304233\pi$
$743$	19.7898	+	4.69027i	0.726018	+	0.172069i	0.149042	+	0.988831i	$0.452381\pi$
$744$	23.6901	+	6.38595i	0.868520	+	0.234120i
$745$	5.26893	+	12.2148i	0.193039	+	0.447514i
$746$	−14.2626	+	0.500729i	−0.522190	+	0.0183330i
$747$	47.8805	−	15.3390i	1.75186	−	0.561224i
$748$	2.46225	−	1.66215i	0.0900289	−	0.0607742i
$749$	2.09737	+	3.18889i	0.0766361	+	0.116520i
$750$	27.8009	+	6.13326i	1.01515	+	0.223955i
$751$	0.625691	−	0.465810i	0.0228318	−	0.0169976i	−0.585682	−	0.810541i	$-0.699173\pi$
$751$	0.625691	−	0.465810i	0.0228318	−	0.0169976i	0.608514	+	0.793543i	$0.291766\pi$
$752$	9.42749	+	9.52358i	0.343785	+	0.347289i
$753$	−5.48754	−	25.3487i	−0.199977	−	0.923760i
$754$	1.98135	+	1.36970i	0.0721566	+	0.0498816i
$755$	−7.06989	−	12.2454i	−0.257300	−	0.445656i
$756$	3.41544	−	0.0397284i	0.124218	−	0.00144491i
$757$	9.48263	−	16.4244i	0.344652	−	0.596955i	−0.640638	−	0.767843i	$-0.721330\pi$
$757$	9.48263	−	16.4244i	0.344652	−	0.596955i	0.985290	+	0.170888i	$0.0546636\pi$
$758$	17.6357	−	8.35295i	0.640558	−	0.303393i
$759$	2.97134	−	1.21349i	0.107853	−	0.0440469i
$760$	1.69215	+	0.873428i	0.0613807	+	0.0316826i
$761$	0.0980942	+	0.839250i	0.00355591	+	0.0304228i	0.994900	−	0.100868i	$-0.0321619\pi$
$761$	0.0980942	+	0.839250i	0.00355591	+	0.0304228i	−0.991344	+	0.131291i	$0.958088\pi$
$762$	5.46857	+	7.11159i	0.198105	+	0.257626i
$763$	2.40450	−	4.78776i	0.0870488	−	0.173328i
$764$	−39.9601	+	2.80929i	−1.44571	+	0.101637i
$765$	0.201500	+	10.5260i	0.00728526	+	0.380569i
$766$	10.2981	+	16.4735i	0.372084	+	0.595212i
$767$	−5.79778	−	0.677663i	−0.209346	−	0.0244690i
$768$	−25.1230	+	11.6976i	−0.906549	+	0.422101i
$769$	−13.2874	−	44.3832i	−0.479158	−	1.60050i	−0.766215	−	0.642584i	$-0.777862\pi$
$769$	−13.2874	−	44.3832i	−0.479158	−	1.60050i	0.287057	−	0.957913i	$-0.407323\pi$
$770$	−0.387984	+	0.212216i	−0.0139820	+	0.00764774i
$771$	−21.0194	−	18.3482i	−0.756996	−	0.660796i
$772$	−15.4198	+	4.81891i	−0.554972	+	0.173436i
$773$	9.41019	+	25.8543i	0.338461	+	0.929914i	0.985832	+	0.167738i	$0.0536464\pi$
$773$	9.41019	+	25.8543i	0.338461	+	0.929914i	−0.647371	+	0.762175i	$0.724131\pi$
$774$	−35.6431	+	15.2085i	−1.28116	+	0.546658i
$775$	−4.71441	+	12.9527i	−0.169347	+	0.465276i
$776$	4.77530	+	28.9536i	0.171423	+	1.03937i
$777$	−0.314460	+	4.03916i	−0.0112812	+	0.144904i
$778$	−27.5870	+	9.32554i	−0.989041	+	0.334337i
$779$	0.230346	−	0.115684i	0.00825301	−	0.00414482i
$780$	1.19551	−	4.88065i	0.0428063	−	0.174755i
$781$	0.590769	−	0.140015i	0.0211394	−	0.00501012i
$782$	2.98531	−	9.19368i	0.106754	−	0.328765i
$783$	−3.12526	−	8.59670i	−0.111688	−	0.307221i
$784$	−26.9697	−	5.71153i	−0.963205	−	0.203983i
$785$	−0.790119	+	0.745439i	−0.0282006	+	0.0266059i
$786$	3.99415	−	39.4980i	0.142467	−	1.40885i
$787$	24.1392	+	1.40595i	0.860468	+	0.0501165i	0.482702	−	0.875785i	$-0.339655\pi$
$787$	24.1392	+	1.40595i	0.860468	+	0.0501165i	0.377766	+	0.925901i	$0.376692\pi$
$788$	19.1915	−	34.1823i	0.683670	−	1.21769i
$789$	4.02650	+	41.4502i	0.143347	+	1.47566i
$790$	−17.7762	−	17.5640i	−0.632449	−	0.624899i
$791$	0.935677	+	5.30649i	0.0332688	+	0.188677i
$792$	5.17074	+	1.50268i	0.183734	+	0.0533955i
$793$	0.809193	−	4.58916i	0.0287353	−	0.162966i
$794$	35.6974	−	25.3164i	1.26685	−	0.898444i
$795$	22.3512	−	3.49278i	0.792715	−	0.123876i
$796$	6.93461	+	36.7423i	0.245791	+	1.30230i
$797$	−37.4007	−	35.2858i	−1.32480	−	1.24989i	−0.945904	−	0.324448i	$-0.894822\pi$
$797$	−37.4007	−	35.2858i	−1.32480	−	1.24989i	−0.378898	−	0.925438i	$-0.623697\pi$
$798$	−0.118345	+	0.341613i	−0.00418937	+	0.0120930i
$799$	−6.29001	−	4.68274i	−0.222525	−	0.165663i
$800$	−5.33855	−	14.6250i	−0.188746	−	0.517072i
$801$	−5.68470	+	20.4016i	−0.200859	+	0.720854i
$802$	−16.6865	+	21.3659i	−0.589220	+	0.754458i
$803$	0.408452	+	7.01285i	0.0144140	+	0.247478i
$804$	31.5157	+	38.1369i	1.11147	+	1.34498i
$805$	−0.569928	+	1.32124i	−0.0200873	+	0.0465676i
$806$	6.38375	+	2.49183i	0.224858	+	0.0877708i
$807$	1.36172	+	35.2061i	0.0479347	+	1.23931i
$808$	11.4930	+	32.6991i	0.404323	+	1.15035i
$809$		−	21.7143i		−	0.763435i	−0.924279	−	0.381718i	$-0.875333\pi$
$809$		−	21.7143i		−	0.763435i	0.924279	−	0.381718i	$-0.124667\pi$
$810$	−14.4299	+	12.4867i	−0.507016	+	0.438738i
$811$		−	44.9815i		−	1.57952i	−0.613419	−	0.789758i	$-0.710206\pi$
$811$		−	44.9815i		−	1.57952i	0.613419	−	0.789758i	$-0.289794\pi$
$812$	−0.148133	−	1.14765i	−0.00519843	−	0.0402748i
$813$	9.98465	−	6.29132i	0.350177	−	0.220646i
$814$	−2.32237	+	5.94964i	−0.0813991	+	0.208535i
$815$	3.73695	−	8.66322i	0.130900	−	0.303460i
$816$	13.5087	−	8.97219i	0.472901	−	0.314089i
$817$	−0.238494	−	4.09478i	−0.00834384	−	0.143258i
$818$	−5.74963	−	4.49037i	−0.201031	−	0.157002i
$819$	0.949497	+	0.0925969i	0.0331781	+	0.00323560i
$820$	1.65467	+	0.473799i	0.0577835	+	0.0165458i
$821$	19.9070	+	14.8202i	0.694758	+	0.517228i	0.885633	−	0.464386i	$-0.153725\pi$
$821$	19.9070	+	14.8202i	0.694758	+	0.517228i	−0.190875	+	0.981614i	$0.561132\pi$
$822$	−2.47599	−	12.8669i	−0.0863602	−	0.448784i
$823$	−27.4416	−	25.8898i	−0.956553	−	0.902462i	0.0387516	−	0.999249i	$-0.487662\pi$
$823$	−27.4416	−	25.8898i	−0.956553	−	0.902462i	−0.995305	+	0.0967872i	$0.969143\pi$
$824$	−33.3878	+	13.9656i	−1.16312	+	0.486514i
$825$	−1.08992	+	2.82190i	−0.0379461	+	0.0982461i
$826$	1.62224	+	2.28745i	0.0564451	+	0.0795905i
$827$	3.03534	−	17.2142i	0.105549	−	0.598598i	−0.885451	−	0.464733i	$-0.846150\pi$
$827$	3.03534	−	17.2142i	0.105549	−	0.598598i	0.991000	−	0.133865i	$-0.0427387\pi$
$828$	16.2693	−	6.50223i	0.565397	−	0.225968i
$829$	8.15628	+	46.2566i	0.283279	+	1.60656i	0.711368	+	0.702820i	$0.248076\pi$
$829$	8.15628	+	46.2566i	0.283279	+	1.60656i	−0.428089	+	0.903737i	$0.640813\pi$
$830$	−24.9750	+	25.2768i	−0.866896	+	0.877370i
$831$	12.5090	−	8.93851i	0.433932	−	0.310073i
$832$	−7.33028	+	2.48557i	−0.254132	+	0.0861716i
$833$	16.1048	+	0.937996i	0.557997	+	0.0324996i
$834$	5.25448	−	7.29241i	0.181948	−	0.252516i
$835$	0.837338	−	0.789987i	0.0289773	−	0.0273386i
$836$	−0.334830	+	0.461216i	−0.0115803	+	0.0159515i
$837$	−14.2922	−	21.7482i	−0.494011	−	0.751726i
$838$	24.4288	+	7.93234i	0.843877	+	0.274018i
$839$	4.81496	−	1.14117i	0.166231	−	0.0393974i	−0.146658	−	0.989187i	$-0.546852\pi$
$839$	4.81496	−	1.14117i	0.166231	−	0.0393974i	0.312888	+	0.949790i	$0.398703\pi$
$840$	−2.12658	+	1.14251i	−0.0733738	+	0.0394204i
$841$	23.1461	−	11.6244i	0.798140	−	0.400841i
$842$	6.68928	+	19.7884i	0.230528	+	0.681952i
$843$	−3.93325	−	2.69836i	−0.135468	−	0.0929365i
$844$	−1.97934	+	42.8417i	−0.0681318	+	1.47467i
$845$	−6.18609	+	16.9961i	−0.212808	+	0.584685i
$846$	−0.770478	−	14.1926i	−0.0264896	−	0.487951i
$847$	1.19127	+	3.27300i	0.0409326	+	0.112461i
$848$	−23.0337	−	26.1485i	−0.790980	−	0.897944i
$849$	−3.86329	+	19.6581i	−0.132588	+	0.674663i
$850$	4.37194	+	7.99300i	0.149956	+	0.274158i
$851$	5.96016	+	19.9083i	0.204312	+	0.682449i
$852$	3.23055	−	0.740077i	0.110677	−	0.0253546i
$853$	−23.2939	−	2.72267i	−0.797568	−	0.0932223i	−0.292459	−	0.956278i	$-0.594474\pi$
$853$	−23.2939	−	2.72267i	−0.797568	−	0.0932223i	−0.505109	+	0.863056i	$0.668548\pi$
$854$	−1.89831	+	1.18669i	−0.0649590	+	0.0406077i
$855$	−0.727006	−	1.88441i	−0.0248631	−	0.0644453i
$856$	9.07123	+	31.5683i	0.310048	+	1.07898i
$857$	17.1653	−	34.1789i	0.586355	−	1.16753i	−0.383431	−	0.923570i	$-0.625258\pi$
$857$	17.1653	−	34.1789i	0.586355	−	1.16753i	0.969786	−	0.243959i	$-0.0784462\pi$
$858$	1.39005	+	0.574101i	0.0474556	+	0.0195995i
$859$	2.92387	+	25.0153i	0.0997611	+	0.853510i	0.946765	+	0.321924i	$0.104330\pi$
$859$	2.92387	+	25.0153i	0.0997611	+	0.853510i	−0.847004	+	0.531586i	$0.821596\pi$
$860$	17.3517	−	21.1906i	0.591687	−	0.722594i
$861$	−0.0442628	+	0.323757i	−0.00150847	+	0.0110336i
$862$	−1.45320	−	3.06816i	−0.0494961	−	0.104502i
$863$	−20.9288	+	36.2497i	−0.712424	+	1.23395i	0.251521	+	0.967852i	$0.419069\pi$
$863$	−20.9288	+	36.2497i	−0.712424	+	1.23395i	−0.963945	+	0.266102i	$0.914264\pi$
$864$	28.1637	+	8.41459i	0.958149	+	0.286270i
$865$	2.44814	+	4.24030i	0.0832392	+	0.144174i
$866$	−1.87815	+	2.71685i	−0.0638220	+	0.0923222i
$867$	14.7794	−	13.4082i	0.501933	−	0.455365i
$868$	−1.16307	−	3.07992i	−0.0394772	−	0.104539i
$869$	5.99934	−	4.46634i	0.203514	−	0.151510i
$870$	4.77087	+	4.36266i	0.161748	+	0.147908i
$871$	7.59317	+	11.5448i	0.257285	+	0.391182i
$872$	32.0090	−	33.1835i	1.08396	−	1.12374i
$873$	16.6025	−	26.3270i	0.561910	−	0.891033i
$874$	0.0650660	+	1.85332i	0.00220089	+	0.0626894i
$875$	−1.51304	−	3.50762i	−0.0511501	−	0.118579i
$876$	1.94214	+	38.2976i	0.0656188	+	1.29395i
$877$	14.8049	+	3.50883i	0.499927	+	0.118485i	0.472840	−	0.881148i	$-0.343229\pi$
$877$	14.8049	+	3.50883i	0.499927	+	0.118485i	0.0270867	+	0.999633i	$0.491377\pi$
$878$	−20.7732	+	34.1355i	−0.701060	+	1.15202i
$879$	32.6823	+	0.637990i	1.10235	+	0.0215189i
$880$	−3.73088	+	0.750662i	−0.125768	+	0.0253048i
$881$	−15.2247	+	18.1441i	−0.512934	+	0.611291i	−0.958895	−	0.283762i	$-0.908418\pi$
$881$	−15.2247	+	18.1441i	−0.512934	+	0.611291i	0.445961	+	0.895052i	$0.352862\pi$
$882$	17.3684	+	23.5229i	0.584824	+	0.792057i
$883$	33.4504	+	39.8647i	1.12570	+	1.34155i	0.932826	+	0.360328i	$0.117335\pi$
$883$	33.4504	+	39.8647i	1.12570	+	1.34155i	0.192871	+	0.981224i	$0.438220\pi$
$884$	4.02290	−	2.08125i	0.135305	−	0.0699999i
$885$	−15.1712	−	3.90987i	−0.509973	−	0.131429i
$886$	47.7034	+	9.55167i	1.60263	+	0.320895i
$887$	−48.2168	−	31.7127i	−1.61896	−	1.06481i	−0.945519	−	0.325566i	$-0.894445\pi$
$887$	−48.2168	−	31.7127i	−1.61896	−	1.06481i	−0.673441	−	0.739241i	$-0.735184\pi$
$888$	−12.9209	+	32.3819i	−0.433598	+	1.08666i
$889$	0.345236	−	1.15317i	0.0115789	−	0.0386761i
$890$	−3.11481	−	14.6406i	−0.104409	−	0.490753i
$891$	−3.04285	−	4.83321i	−0.101939	−	0.161919i
$892$	20.3655	+	45.6957i	0.681887	+	1.53000i
$893$	1.44122	+	0.431474i	0.0482287	+	0.0144387i
$894$	−21.0675	+	5.34095i	−0.704602	+	0.178628i
$895$	9.07419	−	13.7966i	0.303317	−	0.461171i
$896$	3.24412	+	1.81742i	0.108379	+	0.0607158i
$897$	4.71442	−	1.31171i	0.157410	−	0.0437967i
$898$	1.12740	+	4.10868i	0.0376220	+	0.137109i
$899$	−6.75384	+	5.66714i	−0.225253	+	0.189010i
$900$	−6.06518	+	15.3591i	−0.202173	+	0.511972i
$901$	15.6208	+	13.1074i	0.520403	+	0.436670i
$902$	−0.214899	+	0.468171i	−0.00715535	+	0.0155884i
$903$	4.45154	+	2.68728i	0.148138	+	0.0894271i
$904$	−5.89295	+	45.9939i	−0.195997	+	1.52974i
$905$	0.483987	−	2.04210i	0.0160883	−	0.0678817i
$906$	21.5827	−	8.23834i	0.717037	−	0.273700i
$907$	5.25740	−	2.26782i	0.174569	−	0.0753018i	−0.307002	−	0.951709i	$-0.599326\pi$
$907$	5.25740	−	2.26782i	0.174569	−	0.0753018i	0.481571	+	0.876407i	$0.340066\pi$
$908$	−2.87133	−	11.4980i	−0.0952884	−	0.381573i
$909$	13.9122	−	34.0285i	0.461438	−	1.12865i
$910$	−0.625105	+	0.252695i	−0.0207220	+	0.00837674i
$911$	−23.2391	+	15.2846i	−0.769947	+	0.506402i	−0.872672	−	0.488308i	$-0.837614\pi$
$911$	−23.2391	+	15.2846i	−0.769947	+	0.506402i	0.102724	+	0.994710i	$0.467244\pi$
$912$	−1.84663	+	2.50390i	−0.0611479	+	0.0829123i
$913$	−6.35089	−	8.53072i	−0.210184	−	0.282326i
$914$	50.2759	−	7.67298i	1.66298	−	0.253800i
$915$	3.82024	−	11.9094i	0.126293	−	0.393712i
$916$	−2.67417	−	1.11563i	−0.0883569	−	0.0368613i
$917$	−4.61322	+	2.66344i	−0.152342	+	0.0879546i
$918$	−17.0327	−	2.39711i	−0.562164	−	0.0791164i
$919$	−48.9501	−	28.2614i	−1.61472	−	0.932257i	−0.988257	−	0.152803i	$-0.951170\pi$
$919$	−48.9501	−	28.2614i	−1.61472	−	0.932257i	−0.626459	−	0.779454i	$-0.715497\pi$
$920$	−8.06405	+	9.39702i	−0.265864	+	0.309810i
$921$	−11.0891	+	14.3038i	−0.365399	+	0.471325i
$922$	−16.5177	+	13.2225i	−0.543982	+	0.435459i
$923$	0.919410	−	0.107464i	0.0302628	−	0.00353721i
$924$	−0.242010	−	0.680779i	−0.00796153	−	0.0223960i
$925$	−17.5033	−	8.79050i	−0.575506	−	0.289030i
$926$	15.6943	+	2.20270i	0.515747	+	0.0723852i
$927$	36.3160	+	12.4361i	1.19277	+	0.408454i
$928$	1.72005	−	9.80849i	0.0564635	−	0.321979i
$929$	4.22909	−	36.1822i	0.138752	−	1.18710i	−0.727004	−	0.686633i	$-0.759088\pi$
$929$	4.22909	−	36.1822i	0.138752	−	1.18710i	0.865756	−	0.500467i	$-0.166838\pi$
$930$	16.0698	+	8.94715i	0.526950	+	0.293389i
$931$	−2.96491	+	0.887634i	−0.0971709	+	0.0290910i
$932$	16.5988	−	14.2712i	0.543713	−	0.467470i
$933$	15.5354	+	45.4226i	0.508606	+	1.48707i
$934$	4.88248	+	52.1953i	0.159759	+	1.70788i
$935$	2.09267	−	0.761670i	0.0684376	−	0.0249093i
$936$	7.56430	+	3.19081i	0.247247	+	0.104295i
$937$	−55.2556	−	20.1114i	−1.80512	−	0.657011i	−0.997756	−	0.0669616i	$-0.978669\pi$
$937$	−55.2556	−	20.1114i	−1.80512	−	0.657011i	−0.807367	−	0.590049i	$-0.799108\pi$
$938$	1.67961	−	6.42242i	0.0548413	−	0.209699i
$939$	11.8886	+	24.8710i	0.387971	+	0.811635i
$940$	5.12686	+	8.63870i	0.167220	+	0.281763i
$941$	−24.9323	−	49.6443i	−0.812771	−	1.61836i	−0.785605	−	0.618728i	$-0.787648\pi$
$941$	−24.9323	−	49.6443i	−0.812771	−	1.61836i	−0.0271656	−	0.999631i	$-0.508648\pi$
$942$	−0.998208	−	1.46740i	−0.0325234	−	0.0478105i
$943$	0.386545	+	1.63096i	0.0125877	+	0.0531115i
$944$	7.47455	+	22.9459i	0.243276	+	0.746826i
$945$	2.49125	+	0.591431i	0.0810404	+	0.0192393i
$946$	5.48614	+	6.09069i	0.178370	+	0.198025i
$947$	24.2935	+	25.7496i	0.789433	+	0.836750i	0.989725	−	0.142987i	$-0.0456706\pi$
$947$	24.2935	+	25.7496i	0.789433	+	0.836750i	−0.200292	+	0.979736i	$0.564189\pi$
$948$	32.9314	−	24.1343i	1.06956	−	0.783847i
$949$	−0.622748	+	10.6922i	−0.0202153	+	0.347083i
$950$	−1.31264	−	1.15410i	−0.0425878	−	0.0374441i
$951$	14.4421	−	31.7612i	0.468316	−	1.02993i
$952$	−2.03639	−	0.766830i	−0.0659997	−	0.0248531i
$953$	−10.7924	+	1.90300i	−0.349601	+	0.0616441i	−0.345691	−	0.938348i	$-0.612356\pi$
$953$	−10.7924	+	1.90300i	−0.349601	+	0.0616441i	−0.00390973	+	0.999992i	$0.501245\pi$
$954$	−0.145754	+	36.9603i	−0.00471896	+	1.19663i
$955$	−29.5730	−	5.21452i	−0.956960	−	0.168738i
$956$	−44.2021	−	40.7104i	−1.42960	−	1.31667i
$957$	−1.50621	+	1.21456i	−0.0486887	+	0.0392611i
$958$	0.801449	−	34.7123i	0.0258936	−	1.12150i
$959$	−1.20652	+	1.27884i	−0.0389606	+	0.0412958i
$960$	−20.3964	+	3.94468i	−0.658291	+	0.127314i
$961$	3.53320	−	4.74591i	0.113974	−	0.153094i
$962$	−4.56997	+	8.59874i	−0.147342	+	0.277234i
$963$	15.0366	−	31.4261i	0.484549	−	1.01269i
$964$	−16.3717	+	33.5989i	−0.527298	+	1.08215i
$965$	−12.0900	+	0.704162i	−0.389191	+	0.0226678i
$966$	−1.98404	−	1.26110i	−0.0638354	−	0.0405752i
$967$	−21.5115	−	9.27917i	−0.691764	−	0.298398i	0.0210223	−	0.999779i	$-0.493308\pi$
$967$	−21.5115	−	9.27917i	−0.691764	−	0.298398i	−0.712787	+	0.701381i	$0.752567\pi$
$968$	1.41132	+	29.9404i	0.0453615	+	0.962322i
$969$	0.848679	−	1.61069i	0.0272635	−	0.0517427i
$970$	−1.78561	+	21.9251i	−0.0573324	+	0.703972i
$971$	−34.7517			−1.11523			−0.557617	−	0.830098i	$-0.688284\pi$
$971$	−34.7517			−1.11523			−0.557617	+	0.830098i	$0.688284\pi$
$972$	−16.4118	−	26.5076i	−0.526409	−	0.850232i
$973$	−1.20605			−0.0386641
$974$	3.77549	−	46.3585i	0.120975	−	1.48542i
$975$	−2.14999	+	4.08042i	−0.0688549	+	0.130678i
$976$	−18.6340	+	4.89184i	−0.596460	+	0.156584i
$977$	−32.4159	−	13.9829i	−1.03708	−	0.447351i	−0.191662	−	0.981461i	$-0.561388\pi$
$977$	−32.4159	−	13.9829i	−1.03708	−	0.447351i	−0.845415	+	0.534110i	$0.820647\pi$
$978$	13.0091	+	8.26888i	0.415985	+	0.264410i
$979$	4.47235	−	0.260485i	0.142937	−	0.00832513i
$980$	−18.5776	−	9.05231i	−0.593440	−	0.289166i
$981$	−48.7563	+	3.77728i	−1.55667	+	0.120599i
$982$	−1.44954	+	2.72741i	−0.0462566	+	0.0870351i
$983$	3.33520	−	4.47995i	0.106376	−	0.142888i	−0.745747	−	0.666229i	$-0.767907\pi$
$983$	3.33520	−	4.47995i	0.106376	−	0.142888i	0.852123	+	0.523341i	$0.175315\pi$
$984$	−1.19225	+	2.54678i	−0.0380076	+	0.0811884i
$985$	20.1662	−	21.3749i	0.642549	−	0.681062i
$986$	−0.134506	+	5.82572i	−0.00428354	+	0.185529i
$987$	−1.48462	+	1.19716i	−0.0472561	+	0.0381059i
$988$	−0.588683	+	0.639174i	−0.0187285	+	0.0203348i
$989$	26.2668	+	4.63154i	0.835234	+	0.147274i
$990$	3.48773	+	2.03202i	0.110847	+	0.0645819i
$991$	9.64827	−	1.70125i	0.306487	−	0.0540420i	−0.0182893	−	0.999833i	$-0.505822\pi$
$991$	9.64827	−	1.70125i	0.306487	−	0.0540420i	0.324777	+	0.945791i	$0.394711\pi$
$992$	−1.67375	−	28.2819i	−0.0531415	−	0.897951i
$993$	−5.26699	+	11.5832i	−0.167143	+	0.367583i
$994$	−0.333975	−	0.293638i	−0.0105930	−	0.00931363i
$995$	−1.62976	+	27.9820i	−0.0516670	+	0.887088i
$996$	−34.3177	−	46.8267i	−1.08740	−	1.48376i
$997$	−21.8718	−	23.1828i	−0.692688	−	0.734206i	0.281595	−	0.959533i	$-0.409136\pi$
$997$	−21.8718	−	23.1828i	−0.692688	−	0.734206i	−0.974283	+	0.225327i	$0.927655\pi$
$998$	−15.5247	−	17.2355i	−0.491427	−	0.545580i
$999$	33.0523	−	16.5838i	1.04573	−	0.524690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.275.52	yes	936
3.2	odd	2		972.2.p.a.935.1		936
4.3	odd	2	inner	324.2.p.a.275.45	yes	936
12.11	even	2		972.2.p.a.935.8		936
81.38	odd	54	inner	324.2.p.a.119.45	✓	936
81.43	even	27		972.2.p.a.683.8		936
324.43	odd	54		972.2.p.a.683.1		936
324.119	even	54	inner	324.2.p.a.119.52	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.119.45	✓	936	81.38	odd	54	inner
324.2.p.a.119.52	yes	936	324.119	even	54	inner
324.2.p.a.275.45	yes	936	4.3	odd	2	inner
324.2.p.a.275.52	yes	936	1.1	even	1	trivial
972.2.p.a.683.1		936	324.43	odd	54
972.2.p.a.683.8		936	81.43	even	27
972.2.p.a.935.1		936	3.2	odd	2
972.2.p.a.935.8		936	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40955 + 0.114795i) q^{2} +(-0.807404 + 1.53235i) q^{3} +(1.97364 + 0.323618i) q^{4} +(1.37664 + 0.593826i) q^{5} +(-1.31398 + 2.06723i) q^{6} +(0.328117 - 0.0191107i) q^{7} +(2.74479 + 0.682720i) q^{8} +(-1.69620 - 2.47445i) q^{9} +O(q^{10})\)	\(q+(1.40955 + 0.114795i) q^{2} +(-0.807404 + 1.53235i) q^{3} +(1.97364 + 0.323618i) q^{4} +(1.37664 + 0.593826i) q^{5} +(-1.31398 + 2.06723i) q^{6} +(0.328117 - 0.0191107i) q^{7} +(2.74479 + 0.682720i) q^{8} +(-1.69620 - 2.47445i) q^{9} +(1.87228 + 0.995058i) q^{10} +(-0.378950 + 0.509018i) q^{11} +(-2.08942 + 2.76302i) q^{12} +(-0.663958 + 0.703754i) q^{13} +(0.464690 + 0.0107289i) q^{14} +(-2.02146 + 1.63004i) q^{15} +(3.79054 + 1.27741i) q^{16} +(-2.30514 - 0.406459i) q^{17} +(-2.10681 - 3.68257i) q^{18} +(0.442240 - 0.0779788i) q^{19} +(2.52483 + 1.61751i) q^{20} +(-0.235639 + 0.518221i) q^{21} +(-0.592580 + 0.673983i) q^{22} +(-0.169788 + 2.91515i) q^{23} +(-3.26232 + 3.65476i) q^{24} +(-1.88869 - 2.00189i) q^{25} +(-1.01667 + 0.915755i) q^{26} +(5.16125 - 0.601287i) q^{27} +(0.653771 + 0.0684671i) q^{28} +(-0.405970 - 1.71292i) q^{29} +(-3.03646 + 2.06557i) q^{30} +(-2.24773 - 4.47560i) q^{31} +(5.19631 + 2.23571i) q^{32} +(-0.474028 - 0.991667i) q^{33} +(-3.20254 - 0.837541i) q^{34} +(0.463049 + 0.168536i) q^{35} +(-2.54691 - 5.43261i) q^{36} +(6.68750 - 2.43405i) q^{37} +(0.632309 - 0.0591478i) q^{38} +(-0.542316 - 1.58563i) q^{39} +(3.37319 + 2.56979i) q^{40} +(0.549891 - 0.164626i) q^{41} +(-0.391633 + 0.703406i) q^{42} +(1.06039 - 9.07220i) q^{43} +(-0.912640 + 0.881985i) q^{44} +(-0.865666 - 4.41369i) q^{45} +(-0.573969 + 4.08954i) q^{46} +(2.99380 + 1.50354i) q^{47} +(-5.01795 + 4.77705i) q^{48} +(-6.84537 + 0.800109i) q^{49} +(-2.43239 - 3.03857i) q^{50} +(2.48402 - 3.20411i) q^{51} +(-1.53816 + 1.17409i) q^{52} +(-7.54454 - 4.35584i) q^{53} +(7.34404 - 0.255056i) q^{54} +(-0.823948 + 0.475706i) q^{55} +(0.913662 + 0.171557i) q^{56} +(-0.237575 + 0.740627i) q^{57} +(-0.375598 - 2.46104i) q^{58} +(3.60275 + 4.83934i) q^{59} +(-4.51715 + 2.56295i) q^{60} +(-4.02401 + 2.64663i) q^{61} +(-2.65451 - 6.56660i) q^{62} +(-0.603840 - 0.779495i) q^{63} +(7.06779 + 3.74785i) q^{64} +(-1.33194 + 0.574543i) q^{65} +(-0.554327 - 1.45222i) q^{66} +(3.29362 - 13.8969i) q^{67} +(-4.41799 - 1.54819i) q^{68} +(-4.32994 - 2.61388i) q^{69} +(0.633343 + 0.290715i) q^{70} +(-0.732903 - 0.614979i) q^{71} +(-2.96635 - 7.94989i) q^{72} +(8.47993 - 7.11550i) q^{73} +(9.70577 - 2.66322i) q^{74} +(4.59254 - 1.27780i) q^{75} +(0.898060 - 0.0107855i) q^{76} +(-0.114612 + 0.174260i) q^{77} +(-0.582397 - 2.29727i) q^{78} +(-11.2910 - 3.38029i) q^{79} +(4.45967 + 4.00947i) q^{80} +(-3.24583 + 8.39432i) q^{81} +(0.793995 - 0.168924i) q^{82} +(-4.80659 + 16.0551i) q^{83} +(-0.632773 + 0.946526i) q^{84} +(-2.93199 - 1.92840i) q^{85} +(2.53611 - 12.6660i) q^{86} +(2.95258 + 0.760931i) q^{87} +(-1.38766 + 1.13843i) q^{88} +(-4.53781 - 5.40795i) q^{89} +(-0.713526 - 6.32067i) q^{90} +(-0.204407 + 0.243603i) q^{91} +(-1.27850 + 5.69851i) q^{92} +(8.67302 + 0.169306i) q^{93} +(4.04730 + 2.46299i) q^{94} +(0.655113 + 0.155265i) q^{95} +(-7.62141 + 6.15744i) q^{96} +(4.10930 + 9.52643i) q^{97} +(-9.74072 + 0.341976i) q^{98} +(1.90231 + 0.0742983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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