LMFDB - Embedded newform 729.2.k.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68619 - 0.0347299i) q^{2} +(0.113106 - 1.72835i) q^{3} +(5.21506 + 0.134874i) q^{4} +(-1.58849 - 0.486773i) q^{5} +(-0.363851 + 4.63875i) q^{6} +(-0.858532 + 2.14086i) q^{7} +(-8.63515 - 0.335083i) q^{8} +(-2.97441 - 0.390976i) q^{9} +O(q^{10})$	\(q+(-2.68619 - 0.0347299i) q^{2} +(0.113106 - 1.72835i) q^{3} +(5.21506 + 0.134874i) q^{4} +(-1.58849 - 0.486773i) q^{5} +(-0.363851 + 4.63875i) q^{6} +(-0.858532 + 2.14086i) q^{7} +(-8.63515 - 0.335083i) q^{8} +(-2.97441 - 0.390976i) q^{9} +(4.25007 + 1.36273i) q^{10} +(-0.0532624 - 0.0302937i) q^{11} +(0.822967 - 8.99821i) q^{12} +(-1.75154 - 3.92038i) q^{13} +(2.38053 - 5.72094i) q^{14} +(-1.02098 + 2.69041i) q^{15} +(12.7643 + 0.660677i) q^{16} +(-0.964670 - 0.438496i) q^{17} +(7.97625 + 1.15354i) q^{18} +(3.64507 + 5.31464i) q^{19} +(-8.21841 - 2.75279i) q^{20} +(3.60306 + 1.72599i) q^{21} +(0.142021 + 0.0832243i) q^{22} +(-2.15891 + 6.58644i) q^{23} +(-1.55583 + 14.8867i) q^{24} +(-1.85522 - 1.25486i) q^{25} +(4.56882 + 10.5917i) q^{26} +(-1.01217 + 5.09662i) q^{27} +(-4.76604 + 11.0489i) q^{28} +(6.47881 - 4.14219i) q^{29} +(2.83599 - 7.19149i) q^{30} +(-0.464075 - 1.70983i) q^{31} +(-17.0172 - 1.10156i) q^{32} +(-0.0583825 + 0.0886299i) q^{33} +(2.57605 + 1.21139i) q^{34} +(2.40588 - 2.98282i) q^{35} +(-15.4590 - 2.44013i) q^{36} +(8.92374 + 1.75257i) q^{37} +(-9.60675 - 14.4027i) q^{38} +(-6.97392 + 2.58387i) q^{39} +(13.5537 + 4.73563i) q^{40} +(-2.32612 + 0.880858i) q^{41} +(-9.61855 - 4.76147i) q^{42} +(-7.34807 + 3.22614i) q^{43} +(-0.273681 - 0.165167i) q^{44} +(4.53451 + 2.06892i) q^{45} +(6.02797 - 17.6174i) q^{46} +(-0.596755 + 2.19867i) q^{47} +(2.58561 - 21.9866i) q^{48} +(1.21424 + 1.16051i) q^{49} +(4.93989 + 3.43521i) q^{50} +(-0.866987 + 1.61769i) q^{51} +(-8.60565 - 20.6813i) q^{52} +(1.21960 - 1.29270i) q^{53} +(2.89588 - 13.6553i) q^{54} +(0.0698606 + 0.0740479i) q^{55} +(8.13092 - 18.1990i) q^{56} +(9.59785 - 5.69884i) q^{57} +(-17.5471 + 10.9017i) q^{58} +(8.95461 - 1.51932i) q^{59} +(-5.68736 + 13.8930i) q^{60} +(-7.34231 + 13.5124i) q^{61} +(1.18721 + 4.60903i) q^{62} +(3.39065 - 6.03214i) q^{63} +(20.1872 + 1.56907i) q^{64} +(0.873972 + 7.08009i) q^{65} +(0.159904 - 0.236049i) q^{66} +(5.09120 - 2.63986i) q^{67} +(-4.97167 - 2.41689i) q^{68} +(11.1395 + 4.47632i) q^{69} +(-6.56624 + 7.92887i) q^{70} +(9.76121 + 7.56551i) q^{71} +(25.5535 + 4.37281i) q^{72} +(2.81064 - 0.901196i) q^{73} +(-23.9100 - 5.01764i) q^{74} +(-2.37867 + 3.06455i) q^{75} +(18.2924 + 28.2078i) q^{76} +(0.110582 - 0.0880193i) q^{77} +(18.8230 - 6.69855i) q^{78} +(2.10097 - 11.0759i) q^{79} +(-19.9544 - 7.26281i) q^{80} +(8.69428 + 2.32585i) q^{81} +(6.27899 - 2.28536i) q^{82} +(1.41014 + 8.64978i) q^{83} +(18.5574 + 9.48711i) q^{84} +(1.31892 + 1.16612i) q^{85} +(19.8503 - 8.41083i) q^{86} +(-6.42637 - 11.6662i) q^{87} +(0.449778 + 0.279438i) q^{88} +(7.85864 + 3.21061i) q^{89} +(-12.1087 - 5.71500i) q^{90} +(9.89676 - 0.384039i) q^{91} +(-12.1472 + 34.0575i) q^{92} +(-3.00767 + 0.608693i) q^{93} +(1.67936 - 5.88531i) q^{94} +(-3.20313 - 10.2166i) q^{95} +(-3.82864 + 29.2872i) q^{96} +(3.49414 - 15.1796i) q^{97} +(-3.22138 - 3.15951i) q^{98} +(0.146580 + 0.110930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.68619	−	0.0347299i	−1.89942	−	0.0245578i	−0.945665	−	0.325142i	$-0.894588\pi$
$2$	−2.68619	−	0.0347299i	−1.89942	−	0.0245578i	−0.953755	+	0.300584i	$0.902818\pi$
$3$	0.113106	−	1.72835i	0.0653020	−	0.997866i
$3$	0.113106	−	1.72835i	0.0653020	−	0.997866i
$4$	5.21506	+	0.134874i	2.60753	+	0.0674372i
$5$	−1.58849	−	0.486773i	−0.710394	−	0.217691i	−0.0831754	−	0.996535i	$-0.526506\pi$
$5$	−1.58849	−	0.486773i	−0.710394	−	0.217691i	−0.627218	+	0.778844i	$0.715807\pi$
$6$	−0.363851	+	4.63875i	−0.148541	+	1.89376i
$7$	−0.858532	+	2.14086i	−0.324495	+	0.809170i	0.673080	+	0.739569i	$0.264971\pi$
$7$	−0.858532	+	2.14086i	−0.324495	+	0.809170i	−0.997575	+	0.0696005i	$0.977828\pi$
$8$	−8.63515	−	0.335083i	−3.05299	−	0.118470i
$9$	−2.97441	−	0.390976i	−0.991471	−	0.130325i
$10$	4.25007	+	1.36273i	1.34399	+	0.430933i
$11$	−0.0532624	−	0.0302937i	−0.0160592	−	0.00913389i	0.486341	−	0.873769i	$-0.338331\pi$
$11$	−0.0532624	−	0.0302937i	−0.0160592	−	0.00913389i	−0.502400	+	0.864635i	$0.667549\pi$
$12$	0.822967	−	8.99821i	0.237570	−	2.59756i
$13$	−1.75154	−	3.92038i	−0.485791	−	1.08732i	−0.976406	−	0.215943i	$-0.930718\pi$
$13$	−1.75154	−	3.92038i	−0.485791	−	1.08732i	0.490615	−	0.871376i	$-0.336772\pi$
$14$	2.38053	−	5.72094i	0.636223	−	1.52898i
$15$	−1.02098	+	2.69041i	−0.263617	+	0.694662i
$16$	12.7643	+	0.660677i	3.19108	+	0.165169i
$17$	−0.964670	−	0.438496i	−0.233967	−	0.106351i	0.293397	−	0.955991i	$-0.405214\pi$
$17$	−0.964670	−	0.438496i	−0.233967	−	0.106351i	−0.527363	+	0.849640i	$0.676819\pi$
$18$	7.97625	+	1.15354i	1.88002	+	0.271891i
$19$	3.64507	+	5.31464i	0.836235	+	1.21926i	0.973491	+	0.228725i	$0.0734558\pi$
$19$	3.64507	+	5.31464i	0.836235	+	1.21926i	−0.137255	+	0.990536i	$0.543828\pi$
$20$	−8.21841	−	2.75279i	−1.83769	−	0.615544i
$21$	3.60306	+	1.72599i	0.786253	+	0.376642i
$22$	0.142021	+	0.0832243i	0.0302789	+	0.0177435i
$23$	−2.15891	+	6.58644i	−0.450163	+	1.37337i	0.431766	+	0.901986i	$0.357891\pi$
$23$	−2.15891	+	6.58644i	−0.450163	+	1.37337i	−0.881929	+	0.471381i	$0.843756\pi$
$24$	−1.55583	+	14.8867i	−0.317583	+	3.03873i
$25$	−1.85522	−	1.25486i	−0.371044	−	0.250971i
$26$	4.56882	+	10.5917i	0.896019	+	2.07721i
$27$	−1.01217	+	5.09662i	−0.194792	+	0.980845i
$28$	−4.76604	+	11.0489i	−0.900697	+	2.08805i
$29$	6.47881	−	4.14219i	1.20308	−	0.769185i	0.224388	−	0.974500i	$-0.427962\pi$
$29$	6.47881	−	4.14219i	1.20308	−	0.769185i	0.978696	+	0.205315i	$0.0658218\pi$
$30$	2.83599	−	7.19149i	0.517779	−	1.31298i
$31$	−0.464075	−	1.70983i	−0.0833503	−	0.307094i	0.911116	−	0.412150i	$-0.135222\pi$
$31$	−0.464075	−	1.70983i	−0.0833503	−	0.307094i	−0.994466	+	0.105056i	$0.966498\pi$
$32$	−17.0172	−	1.10156i	−3.00825	−	0.194730i
$33$	−0.0583825	+	0.0886299i	−0.0101631	+	0.0154285i
$34$	2.57605	+	1.21139i	0.441790	+	0.207751i
$35$	2.40588	−	2.98282i	0.406668	−	0.504189i
$36$	−15.4590	−	2.44013i	−2.57650	−	0.406689i
$37$	8.92374	+	1.75257i	1.46705	+	0.288120i	0.861530	−	0.507707i	$-0.169507\pi$
$37$	8.92374	+	1.75257i	1.46705	+	0.288120i	0.605524	+	0.795827i	$0.292963\pi$
$38$	−9.60675	−	14.4027i	−1.55842	−	2.33643i
$39$	−6.97392	+	2.58387i	−1.11672	+	0.413750i
$40$	13.5537	+	4.73563i	2.14303	+	0.748769i
$41$	−2.32612	+	0.880858i	−0.363279	+	0.137567i	−0.529035	−	0.848600i	$-0.677446\pi$
$41$	−2.32612	+	0.880858i	−0.363279	+	0.137567i	0.165756	+	0.986167i	$0.446993\pi$
$42$	−9.61855	−	4.76147i	−1.48417	−	0.734711i
$43$	−7.34807	+	3.22614i	−1.12057	+	0.491982i	−0.878244	−	0.478212i	$-0.841285\pi$
$43$	−7.34807	+	3.22614i	−1.12057	+	0.491982i	−0.242326	+	0.970195i	$0.577910\pi$
$44$	−0.273681	−	0.165167i	−0.0412589	−	0.0248999i
$45$	4.53451	+	2.06892i	0.675964	+	0.308417i
$46$	6.02797	−	17.6174i	0.888776	−	2.59755i
$47$	−0.596755	+	2.19867i	−0.0870457	+	0.320709i	−0.995192	−	0.0979440i	$-0.968773\pi$
$47$	−0.596755	+	2.19867i	−0.0870457	+	0.320709i	0.908146	+	0.418653i	$0.137498\pi$
$48$	2.58561	−	21.9866i	0.373201	−	3.17349i
$49$	1.21424	+	1.16051i	0.173463	+	0.165787i
$50$	4.93989	+	3.43521i	0.698606	+	0.485812i
$51$	−0.866987	+	1.61769i	−0.121402	+	0.226522i
$52$	−8.60565	−	20.6813i	−1.19339	−	2.86798i
$53$	1.21960	−	1.29270i	0.167525	−	0.177566i	−0.638172	−	0.769893i	$-0.720309\pi$
$53$	1.21960	−	1.29270i	0.167525	−	0.177566i	0.805697	+	0.592327i	$0.201791\pi$
$54$	2.89588	−	13.6553i	0.394080	−	1.85825i
$55$	0.0698606	+	0.0740479i	0.00942000	+	0.00998461i
$56$	8.13092	−	18.1990i	1.08654	−	2.43194i
$57$	9.59785	−	5.69884i	1.27127	−	0.754830i
$58$	−17.5471	+	10.9017i	−2.30405	+	1.43146i
$59$	8.95461	−	1.51932i	1.16579	−	0.197799i	0.447985	−	0.894041i	$-0.352142\pi$
$59$	8.95461	−	1.51932i	1.16579	−	0.197799i	0.717807	+	0.696242i	$0.245146\pi$
$60$	−5.68736	+	13.8930i	−0.734235	+	1.79357i
$61$	−7.34231	+	13.5124i	−0.940086	+	1.73009i	−0.315945	+	0.948778i	$0.602321\pi$
$61$	−7.34231	+	13.5124i	−0.940086	+	1.73009i	−0.624141	+	0.781312i	$0.714551\pi$
$62$	1.18721	+	4.60903i	0.150776	+	0.585347i
$63$	3.39065	−	6.03214i	0.427182	−	0.759979i
$64$	20.1872	+	1.56907i	2.52340	+	0.196134i
$65$	0.873972	+	7.08009i	0.108403	+	0.878177i
$66$	0.159904	−	0.236049i	0.0196829	−	0.0290556i
$67$	5.09120	−	2.63986i	0.621989	−	0.322511i	−0.120151	−	0.992756i	$-0.538338\pi$
$67$	5.09120	−	2.63986i	0.621989	−	0.322511i	0.742140	+	0.670245i	$0.233811\pi$
$68$	−4.97167	−	2.41689i	−0.602903	−	0.293091i
$69$	11.1395	+	4.47632i	1.34104	+	0.538886i
$70$	−6.56624	+	7.92887i	−0.784816	+	0.947681i
$71$	9.76121	+	7.56551i	1.15844	+	0.897861i	0.996044	−	0.0888643i	$-0.0283237\pi$
$71$	9.76121	+	7.56551i	1.15844	+	0.897861i	0.162399	+	0.986725i	$0.448077\pi$
$72$	25.5535	+	4.37281i	3.01151	+	0.515341i
$73$	2.81064	−	0.901196i	0.328961	−	0.105477i	−0.136256	−	0.990674i	$-0.543507\pi$
$73$	2.81064	−	0.901196i	0.328961	−	0.105477i	0.465217	+	0.885197i	$0.345976\pi$
$74$	−23.9100	−	5.01764i	−2.77948	−	0.583289i
$75$	−2.37867	+	3.06455i	−0.274665	+	0.353863i
$76$	18.2924	+	28.2078i	2.09828	+	3.23565i
$77$	0.110582	−	0.0880193i	0.0126020	−	0.0100307i
$78$	18.8230	−	6.69855i	2.13128	−	0.758461i
$79$	2.10097	−	11.0759i	0.236378	−	1.24614i	−0.641451	−	0.767164i	$-0.721667\pi$
$79$	2.10097	−	11.0759i	0.236378	−	1.24614i	0.877829	−	0.478974i	$-0.158991\pi$
$80$	−19.9544	−	7.26281i	−2.23097	−	0.812007i
$81$	8.69428	+	2.32585i	0.966031	+	0.258428i
$82$	6.27899	−	2.28536i	0.693398	−	0.252376i
$83$	1.41014	+	8.64978i	0.154783	+	0.949437i	0.942697	+	0.333651i	$0.108281\pi$
$83$	1.41014	+	8.64978i	0.154783	+	0.949437i	−0.787914	+	0.615786i	$0.788839\pi$
$84$	18.5574	+	9.48711i	2.02478	+	1.03513i
$85$	1.31892	+	1.16612i	0.143057	+	0.126484i
$86$	19.8503	−	8.41083i	2.14052	−	0.906963i
$87$	−6.42637	−	11.6662i	−0.688980	−	1.25075i
$88$	0.449778	+	0.279438i	0.0479465	+	0.0297882i
$89$	7.85864	+	3.21061i	0.833014	+	0.340324i	0.754264	−	0.656571i	$-0.227994\pi$
$89$	7.85864	+	3.21061i	0.833014	+	0.340324i	0.0787495	+	0.996894i	$0.474907\pi$
$90$	−12.1087	−	5.71500i	−1.27637	−	0.602414i
$91$	9.89676	−	0.384039i	1.03746	−	0.0402583i
$92$	−12.1472	+	34.0575i	−1.26643	+	3.55074i
$93$	−3.00767	+	0.608693i	−0.311881	+	0.0631185i
$94$	1.67936	−	5.88531i	0.173212	−	0.607024i
$95$	−3.20313	−	10.2166i	−0.328634	−	1.04820i
$96$	−3.82864	+	29.2872i	−0.390759	+	2.98911i
$97$	3.49414	−	15.1796i	0.354776	−	1.54125i	−0.419116	−	0.907933i	$-0.637660\pi$
$97$	3.49414	−	15.1796i	0.354776	−	1.54125i	0.773892	−	0.633318i	$-0.218307\pi$
$98$	−3.22138	−	3.15951i	−0.325409	−	0.319158i
$99$	0.146580	+	0.110930i	0.0147319	+	0.0111489i
$100$	−9.50584	−	6.79437i	−0.950584	−	0.679437i
$101$	0.566760	−	3.78391i	0.0563947	−	0.376513i	−0.942687	−	0.333677i	$-0.891710\pi$
$101$	0.566760	−	3.78391i	0.0563947	−	0.376513i	0.999082	−	0.0428362i	$-0.0136394\pi$
$102$	2.38507	−	4.31532i	0.236157	−	0.427280i
$103$	1.56661	+	4.39236i	0.154362	+	0.432792i	0.993870	−	0.110557i	$-0.0352633\pi$
$103$	1.56661	+	4.39236i	0.154362	+	0.432792i	−0.839507	+	0.543348i	$0.817156\pi$
$104$	13.8112	+	34.4400i	1.35430	+	3.37712i
$105$	−4.88326	−	4.49559i	−0.476557	−	0.438725i
$106$	−3.32097	+	3.43008i	−0.322561	+	0.333158i
$107$	0.497462	+	8.54108i	0.0480914	+	0.825698i	0.932987	+	0.359909i	$0.117192\pi$
$107$	0.497462	+	8.54108i	0.0480914	+	0.825698i	−0.884896	+	0.465789i	$0.845771\pi$
$108$	−5.96593	+	26.4426i	−0.574072	+	2.54444i
$109$	−0.696640	+	11.9608i	−0.0667260	+	1.14564i	0.784253	+	0.620441i	$0.213047\pi$
$109$	−0.696640	+	11.9608i	−0.0667260	+	1.14564i	−0.850979	+	0.525200i	$0.823990\pi$
$110$	−0.185087	−	0.201333i	−0.0176473	−	0.0191963i
$111$	4.03839	−	15.2252i	0.383307	−	1.44511i
$112$	−12.3730	+	26.7595i	−1.16914	+	2.52853i
$113$	3.15742	−	2.31904i	0.297025	−	0.218157i	−0.433312	−	0.901244i	$-0.642655\pi$
$113$	3.15742	−	2.31904i	0.297025	−	0.218157i	0.730337	+	0.683087i	$0.239363\pi$
$114$	−25.9795	+	14.9748i	−2.43321	+	1.40252i
$115$	6.63550	−	9.41158i	0.618763	−	0.877635i
$116$	34.3460	−	20.7279i	3.18895	−	1.92454i
$117$	3.67704	+	12.3457i	0.339943	+	1.14136i
$118$	−24.1065	+	3.77019i	−2.21919	+	0.347074i
$119$	1.76696	−	1.68876i	0.161977	−	0.154809i
$120$	9.71786	−	22.8900i	0.887115	−	2.08956i
$121$	−5.62078	−	9.45115i	−0.510980	−	0.859196i
$122$	20.1921	−	36.0419i	1.82811	−	3.26308i
$123$	1.25934	+	4.11999i	0.113550	+	0.371487i
$124$	−2.18956	−	8.97943i	−0.196629	−	0.806377i
$125$	7.55140	+	9.36226i	0.675418	+	0.837386i
$126$	−9.31743	+	16.0857i	−0.830062	+	1.43303i
$127$	−0.0558169	−	2.87791i	−0.00495295	−	0.255373i	−0.994101	−	0.108454i	$-0.965410\pi$
$127$	−0.0558169	−	2.87791i	−0.00495295	−	0.255373i	0.989149	−	0.146919i	$-0.0469357\pi$
$128$	−20.2060	−	1.83362i	−1.78597	−	0.162071i
$129$	4.74481	+	13.0650i	0.417757	+	1.15031i
$130$	−2.10176	−	19.0488i	−0.184337	−	1.67069i
$131$	13.3552	−	1.21194i	1.16685	−	0.105887i	0.510181	−	0.860067i	$-0.329578\pi$
$131$	13.3552	−	1.21194i	1.16685	−	0.105887i	0.656668	+	0.754180i	$0.271965\pi$
$132$	−0.316422	+	0.454336i	−0.0275410	+	0.0395448i
$133$	−14.5073	+	3.24080i	−1.25794	+	0.281013i
$134$	−13.7676	+	6.91434i	−1.18934	+	0.597308i
$135$	4.08871	−	7.60322i	0.351901	−	0.654381i
$136$	8.18314	+	4.10973i	0.701698	+	0.352406i
$137$	1.34826	+	0.338012i	0.115190	+	0.0288783i	0.300342	−	0.953832i	$-0.402899\pi$
$137$	1.34826	+	0.338012i	0.115190	+	0.0288783i	−0.185152	+	0.982710i	$0.559278\pi$
$138$	−29.7673	−	12.4111i	−2.53396	−	1.05650i
$139$	4.76673	+	0.682494i	0.404309	+	0.0578884i	0.340901	−	0.940099i	$-0.389268\pi$
$139$	4.76673	+	0.682494i	0.404309	+	0.0578884i	0.0634083	+	0.997988i	$0.479803\pi$
$140$	12.9491	−	15.2311i	1.09440	−	1.28726i
$141$	3.73258	+	1.28009i	0.314340	+	0.107803i
$142$	−25.9577	−	20.6614i	−2.17832	−	1.73386i
$143$	−0.0254715	+	0.261870i	−0.00213003	+	0.0218987i
$144$	−37.7081	−	6.95567i	−3.14234	−	0.579639i
$145$	−12.3078	+	3.42611i	−1.02211	+	0.284523i
$146$	−7.58121	+	2.32317i	−0.627425	+	0.192267i
$147$	2.14311	−	1.96738i	0.176760	−	0.162267i
$148$	46.3015	+	10.3433i	3.80596	+	0.850216i
$149$	−17.4586	+	4.37690i	−1.43027	+	0.358570i	−0.879424	−	0.476040i	$-0.842072\pi$
$149$	−17.4586	+	4.37690i	−1.43027	+	0.358570i	−0.550842	+	0.834610i	$0.685693\pi$
$150$	6.49599	−	8.14933i	0.530395	−	0.665390i
$151$	2.86305	+	3.36759i	0.232991	+	0.274051i	0.865946	−	0.500138i	$-0.166718\pi$
$151$	2.86305	+	3.36759i	0.232991	+	0.274051i	−0.632954	+	0.774189i	$0.718158\pi$
$152$	−29.6949	−	47.1141i	−2.40857	−	3.82146i
$153$	2.69789	+	1.68143i	0.218111	+	0.135936i
$154$	−0.300101	+	0.232596i	−0.0241828	+	0.0187431i
$155$	−0.0951192	+	2.94194i	−0.00764016	+	0.236302i
$156$	−36.7179	+	12.5344i	−2.93979	+	1.00356i
$157$	−0.457223	+	3.70398i	−0.0364903	+	0.295610i	0.963154	+	0.268950i	$0.0866765\pi$
$157$	−0.457223	+	3.70398i	−0.0364903	+	0.295610i	−0.999645	+	0.0266603i	$0.991513\pi$
$158$	−6.02827	+	29.6790i	−0.479584	+	2.36114i
$159$	−2.09630	−	2.25411i	−0.166247	−	0.178763i
$160$	26.4955	+	10.0333i	2.09465	+	0.793205i
$161$	−12.2472	−	10.2766i	−0.965212	−	0.809909i
$162$	−23.2737	−	6.54961i	−1.82855	−	0.514586i
$163$	−2.38453	+	2.00086i	−0.186771	+	0.156719i	−0.731379	−	0.681971i	$-0.761123\pi$
$163$	−2.38453	+	2.00086i	−0.186771	+	0.156719i	0.544608	+	0.838691i	$0.316678\pi$
$164$	−12.2497	+	4.27999i	−0.956538	+	0.334211i
$165$	0.135883	−	0.112368i	0.0105784	−	0.00874787i
$166$	−3.48750	−	23.2839i	−0.270682	−	1.80718i
$167$	−6.05074	+	11.8563i	−0.468221	+	0.917468i	0.529390	+	0.848379i	$0.322421\pi$
$167$	−6.05074	+	11.8563i	−0.468221	+	0.917468i	−0.997610	+	0.0690893i	$0.977991\pi$
$168$	−30.5346	−	16.1115i	−2.35580	−	1.24303i
$169$	−3.62782	+	4.05011i	−0.279063	+	0.311547i
$170$	−3.50236	−	3.17822i	−0.268619	−	0.243759i
$171$	−8.76404	−	17.2331i	−0.670203	−	1.31785i
$172$	−38.7558	+	15.8335i	−2.95510	+	1.20729i
$173$	−9.59342	−	1.62771i	−0.729374	−	0.123752i	−0.209273	−	0.977857i	$-0.567110\pi$
$173$	−9.59342	−	1.62771i	−0.729374	−	0.123752i	−0.520101	+	0.854105i	$0.674106\pi$
$174$	16.8573	+	31.5607i	1.27795	+	2.39261i
$175$	4.27924	−	2.89444i	0.323480	−	0.218799i
$176$	−0.659845	−	0.421868i	−0.0497377	−	0.0317995i
$177$	−1.61310	−	15.6486i	−0.121248	−	1.17622i
$178$	−20.9983	−	8.89722i	−1.57389	−	0.666875i
$179$	−0.650990	−	1.36143i	−0.0486573	−	0.101758i	0.876403	−	0.481579i	$-0.159936\pi$
$179$	−0.650990	−	1.36143i	−0.0486573	−	0.101758i	−0.925060	+	0.379820i	$0.875986\pi$
$180$	23.3687	+	11.4011i	1.74180	+	0.849791i
$181$	−9.44596	−	2.62946i	−0.702113	−	0.195446i	−0.101323	−	0.994854i	$-0.532308\pi$
$181$	−9.44596	−	2.62946i	−0.702113	−	0.195446i	−0.600790	+	0.799407i	$0.705147\pi$
$182$	−26.5979	+	0.687887i	−1.97157	+	0.0509896i
$183$	22.5238	+	14.2184i	1.66501	+	1.05106i
$184$	20.8495	−	56.1515i	1.53705	−	4.13954i
$185$	−13.3222	−	7.12777i	−0.979465	−	0.524044i
$186$	8.10031	−	1.53061i	0.593944	−	0.112229i
$187$	0.0380970	+	0.0525788i	0.00278592	+	0.00384494i
$188$	−3.40866	+	11.3857i	−0.248602	+	0.830388i
$189$	−10.0422	−	6.54253i	−0.730461	−	0.475899i
$190$	8.24937	+	27.5548i	0.598472	+	1.99904i
$191$	−7.44611	+	9.73650i	−0.538781	+	0.704508i	−0.981351	−	0.192226i	$-0.938429\pi$
$191$	−7.44611	+	9.73650i	−0.538781	+	0.704508i	0.442569	+	0.896734i	$0.354067\pi$
$192$	4.99522	−	34.7132i	0.360499	−	2.50521i
$193$	−8.53079	+	4.01159i	−0.614060	+	0.288761i	−0.707334	−	0.706880i	$-0.750102\pi$
$193$	−8.53079	+	4.01159i	−0.614060	+	0.288761i	0.0932740	+	0.995640i	$0.470267\pi$
$194$	−9.91310	+	40.6538i	−0.711719	+	2.91877i
$195$	12.3358	−	0.709729i	0.883382	−	0.0508247i
$196$	6.17583	+	6.21588i	0.441131	+	0.443992i
$197$	21.2457	−	4.17252i	1.51369	−	0.297280i	0.634192	−	0.773175i	$-0.281333\pi$
$197$	21.2457	−	4.17252i	1.51369	−	0.297280i	0.879502	+	0.475895i	$0.157876\pi$
$198$	−0.389889	−	0.303070i	−0.0277082	−	0.0215383i
$199$	7.56867	−	4.17621i	0.536529	−	0.296044i	−0.191613	−	0.981471i	$-0.561372\pi$
$199$	7.56867	−	4.17621i	0.536529	−	0.296044i	0.728142	+	0.685427i	$0.240384\pi$
$200$	15.5996	+	11.4575i	1.10306	+	0.810169i
$201$	−3.98677	−	9.09798i	−0.281205	−	0.641722i
$202$	−1.65384	+	10.1446i	−0.116364	+	0.713772i
$203$	3.30559	+	17.4264i	0.232007	+	1.22310i
$204$	−4.73957	+	8.31943i	−0.331836	+	0.582477i
$205$	4.12379	−	0.266941i	0.288018	−	0.0186440i
$206$	−4.05565	−	11.8531i	−0.282571	−	0.825844i
$207$	8.99662	−	18.7467i	0.625308	−	1.30299i
$208$	−19.7672	−	51.1983i	−1.37061	−	3.54996i
$209$	−0.0331450	−	0.393493i	−0.00229269	−	0.0272185i
$210$	12.9612	+	12.2456i	0.894408	+	0.845026i
$211$	−9.11290	+	13.6623i	−0.627358	+	0.940552i	0.372563	+	0.928007i	$0.378479\pi$
$211$	−9.11290	+	13.6623i	−0.627358	+	0.940552i	−0.999921	+	0.0125452i	$0.996007\pi$
$212$	6.53463	−	6.57701i	0.448800	−	0.451711i
$213$	14.1799	−	16.0151i	0.971593	−	1.09734i
$214$	−1.03964	−	22.9602i	−0.0710685	−	1.56953i
$215$	13.2427	−	1.54785i	0.903147	−	0.105563i
$216$	10.4480	−	43.6709i	0.710899	−	2.97143i
$217$	4.05892	+	0.474420i	0.275538	+	0.0322057i
$218$	2.28670	−	32.1049i	0.154875	−	2.17442i
$219$	−1.23968	−	4.95972i	−0.0837701	−	0.335147i
$220$	0.354340	+	0.395586i	0.0238896	+	0.0266704i
$221$	−0.0294119	+	4.54992i	−0.00197846	+	0.306061i
$222$	−11.3766	+	40.7574i	−0.763549	+	2.73545i
$223$	−1.25518	+	1.10977i	−0.0840532	+	0.0743156i	−0.703362	−	0.710832i	$-0.748318\pi$
$223$	−1.25518	+	1.10977i	−0.0840532	+	0.0743156i	0.619308	+	0.785148i	$0.287413\pi$
$224$	16.9681	−	35.4858i	1.13373	−	2.37100i
$225$	5.02758	+	4.45781i	0.335172	+	0.297187i
$226$	−8.56197	+	6.11973i	−0.569534	+	0.407078i
$227$	−10.9027	−	21.3636i	−0.723637	−	1.41795i	−0.901006	−	0.433807i	$-0.857170\pi$
$227$	−10.9027	−	21.3636i	−0.723637	−	1.41795i	0.177369	−	0.984144i	$-0.443241\pi$
$228$	50.8220	−	28.4253i	3.36577	−	1.88251i
$229$	16.9024	+	22.1015i	1.11694	+	1.46051i	0.871040	+	0.491212i	$0.163446\pi$
$229$	16.9024	+	22.1015i	1.11694	+	1.46051i	0.245901	+	0.969295i	$0.420916\pi$
$230$	−18.1510	+	25.0508i	−1.19684	+	1.65180i
$231$	−0.139621	−	0.201081i	−0.00918639	−	0.0132301i
$232$	−57.3335	+	33.5975i	−3.76413	+	2.20578i
$233$	1.84124	+	8.50011i	0.120624	+	0.556860i	0.997146	+	0.0754992i	$0.0240550\pi$
$233$	1.84124	+	8.50011i	0.120624	+	0.556860i	−0.876522	+	0.481361i	$0.840143\pi$
$234$	−9.44846	−	33.2904i	−0.617665	−	2.17626i
$235$	2.01819	−	3.20208i	0.131652	−	0.208881i
$236$	46.9038	−	6.71561i	3.05317	−	0.437149i
$237$	−18.9055	−	4.88398i	−1.22804	−	0.317249i
$238$	−4.80503	+	4.47496i	−0.311464	+	0.290069i
$239$	8.40779	+	15.4733i	0.543855	+	1.00088i	0.994150	+	0.108004i	$0.0344461\pi$
$239$	8.40779	+	15.4733i	0.543855	+	1.00088i	−0.450296	+	0.892879i	$0.648681\pi$
$240$	−14.8097	+	33.6668i	−0.955960	+	2.17318i
$241$	−8.31840	+	13.9871i	−0.535836	+	0.900990i	0.464049	+	0.885809i	$0.346396\pi$
$241$	−8.31840	+	13.9871i	−0.535836	+	0.900990i	−0.999885	+	0.0151805i	$0.995168\pi$
$242$	14.7702	+	25.5828i	0.949465	+	1.64452i
$243$	5.00327	−	14.7637i	0.320960	−	0.947093i
$244$	−40.1130	+	69.4778i	−2.56797	+	4.44786i
$245$	−1.36391	−	2.43451i	−0.0871370	−	0.155535i
$246$	−3.23972	−	11.1108i	−0.206557	−	0.708399i
$247$	14.4509	−	23.5989i	0.919490	−	1.50156i
$248$	3.43442	+	14.9201i	0.218086	+	0.947428i
$249$	15.1094	−	1.45888i	0.957518	−	0.0924526i
$250$	−19.9593	−	25.4110i	−1.26234	−	1.60714i
$251$	−10.1874	−	19.3403i	−0.643022	−	1.22075i	−0.962017	−	0.272991i	$-0.911987\pi$
$251$	−10.1874	−	19.3403i	−0.643022	−	1.22075i	0.318994	−	0.947757i	$-0.396655\pi$
$252$	18.4960	−	31.0007i	1.16514	−	1.95286i
$253$	0.314516	−	0.285408i	0.0197735	−	0.0179435i
$254$	0.0499852	+	7.73253i	0.00313635	+	0.485182i
$255$	2.16465	−	2.14766i	0.135556	−	0.134492i
$256$	13.9336	+	1.44627i	0.870849	+	0.0903918i
$257$	−27.5366	+	3.58000i	−1.71769	+	0.223314i	−0.923295	−	0.384093i	$-0.874514\pi$
$257$	−27.5366	+	3.58000i	−1.71769	+	0.223314i	−0.794391	+	0.607407i	$0.792210\pi$
$258$	−12.2917	−	35.2597i	−0.765247	−	2.19517i
$259$	−11.4133	+	17.5999i	−0.709189	+	1.09360i
$260$	3.60289	+	37.0410i	0.223442	+	2.29718i
$261$	−20.8901	+	9.78753i	−1.29307	+	0.605833i
$262$	−35.9166	+	2.79166i	−2.21894	+	0.172469i
$263$	5.75711	+	28.3440i	0.354999	+	1.74777i	0.621017	+	0.783797i	$0.286720\pi$
$263$	5.75711	+	28.3440i	0.354999	+	1.74777i	−0.266018	+	0.963968i	$0.585708\pi$
$264$	0.533841	−	0.745769i	0.0328556	−	0.0458989i
$265$	−2.56657	+	1.45977i	−0.157663	+	0.0896730i
$266$	39.0819	−	8.20155i	2.39626	−	0.502869i
$267$	6.43793	−	13.2194i	0.393995	−	0.809012i
$268$	26.9070	−	13.0804i	1.64360	−	0.799010i
$269$	−15.4954	+	20.8140i	−0.944773	+	1.26905i	0.0183058	+	0.999832i	$0.494173\pi$
$269$	−15.4954	+	20.8140i	−0.944773	+	1.26905i	−0.963079	+	0.269218i	$0.913235\pi$
$270$	−11.2471	+	20.2817i	−0.684477	+	1.23430i
$271$	0.147974	+	0.198763i	0.00898877	+	0.0120740i	0.806595	−	0.591105i	$-0.201308\pi$
$271$	0.147974	+	0.198763i	0.00898877	+	0.0120740i	−0.797606	+	0.603179i	$0.793901\pi$
$272$	−12.0237	−	6.23445i	−0.729042	−	0.378019i
$273$	0.455631	−	17.1485i	0.0275761	−	1.03788i
$274$	−3.60995	−	0.954788i	−0.218085	−	0.0576808i
$275$	0.0607993	+	0.123038i	0.00366634	+	0.00741948i
$276$	57.4894	+	24.8467i	3.46046	+	1.49560i
$277$	22.0166	−	15.3104i	1.32285	−	0.919914i	0.323201	−	0.946330i	$-0.395241\pi$
$277$	22.0166	−	15.3104i	1.32285	−	0.919914i	0.999651	+	0.0264167i	$0.00840968\pi$
$278$	−12.7806	−	1.99885i	−0.766531	−	0.119883i
$279$	0.711850	+	5.26717i	0.0426173	+	0.315337i
$280$	−21.7746	+	24.9510i	−1.30128	+	1.49111i
$281$	−3.76319	+	7.61548i	−0.224493	+	0.454301i	−0.979508	−	0.201407i	$-0.935449\pi$
$281$	−3.76319	+	7.61548i	−0.224493	+	0.454301i	0.755014	+	0.655708i	$0.227630\pi$
$282$	−9.98196	−	3.56819i	−0.594417	−	0.212482i
$283$	−21.2202	+	18.2785i	−1.26141	+	1.08654i	−0.269055	+	0.963125i	$0.586711\pi$
$283$	−21.2202	+	18.2785i	−1.26141	+	1.08654i	−0.992355	+	0.123420i	$0.960614\pi$
$284$	49.8849	+	40.7711i	2.96012	+	2.41932i
$285$	−18.0201	+	4.38058i	−1.06742	+	0.259483i
$286$	0.0775159	−	0.702547i	0.00458361	−	0.0415424i
$287$	0.111252	−	5.73615i	0.00656703	−	0.338594i
$288$	50.1856	+	9.92982i	2.95721	+	0.585120i
$289$	−10.4396	−	11.9624i	−0.614091	−	0.703671i
$290$	33.1801	−	8.77573i	1.94840	−	0.515329i
$291$	−25.8404	−	7.75602i	−1.51479	−	0.454666i
$292$	14.7792	−	4.32071i	0.864888	−	0.252850i
$293$	−0.925496	+	10.9874i	−0.0540681	+	0.641889i	0.916337	+	0.400407i	$0.131131\pi$
$293$	−0.925496	+	10.9874i	−0.0540681	+	0.641889i	−0.970405	+	0.241482i	$0.922367\pi$
$294$	−5.82511	+	5.21032i	−0.339727	+	0.303872i
$295$	−14.9639	−	1.94543i	−0.871230	−	0.113268i
$296$	−76.4706	−	18.1239i	−4.44477	−	1.05343i
$297$	0.208306	−	0.240796i	0.0120871	−	0.0139724i
$298$	47.0491	−	11.1508i	2.72548	−	0.645951i
$299$	29.6028	−	3.07269i	1.71197	−	0.177698i
$300$	−12.8182	+	15.6610i	−0.740062	+	0.904187i
$301$	−0.598176	−	18.5010i	−0.0344783	−	1.06638i
$302$	−7.57372	−	9.14542i	−0.435819	−	0.526260i
$303$	−6.47584	−	1.40755i	−0.372027	−	0.0808614i
$304$	43.0156	+	70.2460i	2.46711	+	4.02888i
$305$	18.2406	−	17.8903i	1.04446	−	1.02440i
$306$	−7.18863	−	4.61034i	−0.410946	−	0.263555i
$307$	−5.87202	+	8.56162i	−0.335134	+	0.488637i	−0.955220	−	0.295896i	$-0.904382\pi$
$307$	−5.87202	+	8.56162i	−0.335134	+	0.488637i	0.620086	+	0.784534i	$0.287098\pi$
$308$	0.588564	−	0.444111i	0.0335365	−	0.0253056i
$309$	7.76874	−	2.21085i	0.441948	−	0.125771i
$310$	0.357681	−	7.89929i	0.0203149	−	0.448649i
$311$	0.0832379	+	1.16864i	0.00471999	+	0.0662677i	0.999283	−	0.0378730i	$-0.0120582\pi$
$311$	0.0832379	+	1.16864i	0.00471999	+	0.0662677i	−0.994563	+	0.104141i	$0.966791\pi$
$312$	61.0867	−	19.9752i	3.45835	−	1.13088i
$313$	8.92956	+	24.0489i	0.504729	+	1.35933i	0.898037	+	0.439919i	$0.144993\pi$
$313$	8.92956	+	24.0489i	0.504729	+	1.35933i	−0.393309	+	0.919407i	$0.628670\pi$
$314$	1.35682	−	9.93371i	0.0765700	−	0.560592i
$315$	−8.32230	+	7.93151i	−0.468908	+	0.446890i
$316$	12.4506	−	57.4782i	0.700399	−	3.23340i
$317$	−6.59165	−	20.1100i	−0.370224	−	1.12949i	−0.949342	−	0.314244i	$-0.898249\pi$
$317$	−6.59165	−	20.1100i	−0.370224	−	1.12949i	0.579118	−	0.815244i	$-0.303397\pi$
$318$	5.55276	+	6.12777i	0.311383	+	0.343628i
$319$	−0.470559	+	0.0243559i	−0.0263462	+	0.00136367i
$320$	−31.3034	−	12.3190i	−1.74991	−	0.688655i
$321$	14.8183	+	0.106262i	0.827076	+	0.00593097i
$322$	32.5413	+	28.0302i	1.81345	+	1.56206i
$323$	−1.18584	−	6.72522i	−0.0659817	−	0.374201i
$324$	45.0275	+	13.3021i	2.50153	+	0.739004i
$325$	−1.67001	+	9.47112i	−0.0926357	+	0.525363i
$326$	6.47477	−	5.29186i	0.358605	−	0.293089i
$327$	20.5938	+	2.55689i	1.13884	+	0.141396i
$328$	20.3816	−	6.82690i	1.12538	−	0.376953i
$329$	−4.19472	−	3.16520i	−0.231262	−	0.174503i
$330$	−0.368908	+	0.297123i	−0.0203077	+	0.0163561i
$331$	−12.7830	+	6.83928i	−0.702616	+	0.375921i	−0.783999	−	0.620762i	$-0.786823\pi$
$331$	−12.7830	+	6.83928i	−0.702616	+	0.375921i	0.0813833	+	0.996683i	$0.474066\pi$
$332$	6.18733	+	45.2993i	0.339574	+	2.48612i
$333$	−25.8577	−	8.70183i	−1.41699	−	0.476857i
$334$	16.6652	−	31.6381i	0.911879	−	1.73116i
$335$	−9.37232	+	1.71513i	−0.512065	+	0.0937078i
$336$	44.8504	+	24.4116i	2.44679	+	1.33176i
$337$	6.20060	+	6.40432i	0.337768	+	0.348865i	0.865828	−	0.500342i	$-0.166792\pi$
$337$	6.20060	+	6.40432i	0.337768	+	0.348865i	−0.528060	+	0.849207i	$0.677080\pi$
$338$	9.88566	−	10.7534i	0.537709	−	0.584906i
$339$	−3.65100	−	5.71944i	−0.198295	−	0.310638i
$340$	6.72096	+	6.25928i	0.364495	+	0.339457i
$341$	−0.0270792	+	0.105128i	−0.00146642	+	0.00569300i
$342$	22.9433	+	46.5956i	1.24063	+	2.51960i
$343$	−18.2258	+	8.28464i	−0.984101	+	0.447329i
$344$	64.5328	−	25.3960i	3.47937	−	1.36926i
$345$	−15.5160	−	12.5330i	−0.835355	−	0.674754i
$346$	25.7132	+	4.70551i	1.38235	+	0.252970i
$347$	4.30582	−	5.48193i	0.231149	−	0.294285i	−0.656954	−	0.753931i	$-0.728155\pi$
$347$	4.30582	−	5.48193i	0.231149	−	0.294285i	0.888102	+	0.459646i	$0.152024\pi$
$348$	−31.9404	−	61.7065i	−1.71219	−	3.30782i
$349$	7.20270	+	25.2419i	0.385552	+	1.35117i	0.877096	+	0.480316i	$0.159478\pi$
$349$	7.20270	+	25.2419i	0.385552	+	1.35117i	−0.491544	+	0.870853i	$0.663567\pi$
$350$	−11.5954	+	7.62639i	−0.619798	+	0.407648i
$351$	21.7536	−	4.95886i	1.16112	−	0.264684i
$352$	0.873008	+	0.574186i	0.0465315	+	0.0306042i
$353$	5.75030	−	18.3409i	0.306058	−	0.976189i	−0.666889	−	0.745157i	$-0.732374\pi$
$353$	5.75030	−	18.3409i	0.306058	−	0.976189i	0.972946	−	0.231031i	$-0.0742100\pi$
$354$	3.78962	+	42.0910i	0.201416	+	2.23711i
$355$	−11.8229	−	16.7692i	−0.627494	−	0.890018i
$356$	40.5502	+	17.8034i	2.14916	+	0.943580i
$357$	−2.71892	−	3.24494i	−0.143901	−	0.171741i
$358$	1.70140	+	3.67966i	0.0899217	+	0.194476i
$359$	25.1535	+	13.8791i	1.32755	+	0.732512i	0.978822	−	0.204711i	$-0.0656254\pi$
$359$	25.1535	+	13.8791i	1.32755	+	0.732512i	0.348730	+	0.937223i	$0.386613\pi$
$360$	−38.4629	−	19.3849i	−2.02717	−	1.02167i
$361$	−8.11548	+	21.0196i	−0.427130	+	1.10630i
$362$	25.2823	+	7.39128i	1.32881	+	0.388477i
$363$	−16.9707	+	8.64571i	−0.890730	+	0.453782i
$364$	51.6640	−	0.667968i	2.70793	−	0.0350110i
$365$	−4.90335	+	0.0633958i	−0.256653	+	0.00331829i
$366$	−60.0093	−	38.9756i	−3.13674	−	2.03729i
$367$	19.2252	+	5.62049i	1.00355	+	0.293387i	0.740980	−	0.671527i	$-0.234361\pi$
$367$	19.2252	+	5.62049i	1.00355	+	0.293387i	0.262566	+	0.964914i	$0.415431\pi$
$368$	−31.9085	+	82.6451i	−1.66335	+	4.30818i
$369$	7.26324	−	1.71058i	0.378109	−	0.0890493i
$370$	35.5383	+	19.6092i	1.84755	+	1.01943i
$371$	1.72043	+	3.72082i	0.0893201	+	0.193175i
$372$	−15.7673	+	2.76871i	−0.817496	+	0.143551i
$373$	−7.96070	−	3.49511i	−0.412189	−	0.180970i	0.185597	−	0.982626i	$-0.440578\pi$
$373$	−7.96070	−	3.49511i	−0.412189	−	0.180970i	−0.597786	+	0.801656i	$0.703953\pi$
$374$	−0.100509	−	0.142559i	−0.00519722	−	0.00737157i
$375$	17.0354	−	11.9926i	0.879705	−	0.619293i
$376$	5.88981	−	18.7859i	0.303744	−	0.968809i
$377$	−27.5869	−	18.1442i	−1.42080	−	0.934473i
$378$	26.7479	+	17.9232i	1.37577	+	0.921870i
$379$	−2.24232	+	1.47480i	−0.115180	+	0.0757553i	−0.605792	−	0.795623i	$-0.707144\pi$
$379$	−2.24232	+	1.47480i	−0.115180	+	0.0757553i	0.490612	+	0.871378i	$0.336773\pi$
$380$	−15.3265	−	53.7120i	−0.786235	−	2.75537i
$381$	−4.98035	−	0.229038i	−0.255151	−	0.0117340i
$382$	20.3398	−	25.8954i	1.04067	−	1.32493i
$383$	−13.6883	−	2.50495i	−0.699437	−	0.127997i	−0.181469	−	0.983397i	$-0.558085\pi$
$383$	−13.6883	−	2.50495i	−0.699437	−	0.127997i	−0.517968	+	0.855400i	$0.673312\pi$
$384$	−5.45457	+	34.7157i	−0.278353	+	1.77158i
$385$	−0.218504	+	0.0859894i	−0.0111360	+	0.00438242i
$386$	23.0546	−	10.4796i	1.17345	−	0.533398i
$387$	23.1176	−	6.72297i	1.17513	−	0.341748i
$388$	20.2695	−	78.6910i	1.02903	−	3.99493i
$389$	−21.8200	−	20.3212i	−1.10632	−	1.03032i	−0.999350	−	0.0360610i	$-0.988519\pi$
$389$	−21.8200	−	20.3212i	−1.10632	−	1.03032i	−0.106970	−	0.994262i	$-0.534115\pi$
$390$	−33.1608	+	1.47804i	−1.67916	+	0.0748437i
$391$	4.97076	−	5.40706i	0.251382	−	0.273447i
$392$	−10.0963	−	10.4280i	−0.509941	−	0.526695i
$393$	−0.584096	−	23.2196i	−0.0294638	−	1.17127i
$394$	−57.2148	+	10.4703i	−2.88244	+	0.527486i
$395$	−8.72883	+	16.5713i	−0.439195	+	0.833791i
$396$	0.749463	+	0.598278i	0.0376619	+	0.0300646i
$397$	2.19533	+	16.0727i	0.110180	+	0.806663i	0.960081	+	0.279721i	$0.0902419\pi$
$397$	2.19533	+	16.0727i	0.110180	+	0.806663i	−0.849901	+	0.526942i	$0.823338\pi$
$398$	−20.4759	+	10.9552i	−1.02636	+	0.549136i
$399$	3.96038	+	25.4403i	0.198267	+	1.27361i
$400$	−22.8516	−	17.2431i	−1.14258	−	0.862155i
$401$	−0.681385	+	0.228233i	−0.0340267	+	0.0113974i	−0.334573	−	0.942370i	$-0.608592\pi$
$401$	−0.681385	+	0.228233i	−0.0340267	+	0.0113974i	0.300547	+	0.953767i	$0.402831\pi$
$402$	10.3932	+	24.5773i	0.518367	+	1.22581i
$403$	−5.89033	+	4.81419i	−0.293418	+	0.239812i
$404$	3.46604	−	19.6569i	0.172442	−	0.977967i
$405$	−12.6786	−	7.92672i	−0.630005	−	0.393882i
$406$	−8.27422	−	46.9254i	−0.410643	−	2.32887i
$407$	−0.422208	−	0.363679i	−0.0209281	−	0.0180269i
$408$	8.02863	−	13.6785i	0.397476	−	0.677188i
$409$	−21.1490	−	8.32291i	−1.04575	−	0.411541i	−0.219954	−	0.975510i	$-0.570591\pi$
$409$	−21.1490	−	8.32291i	−1.04575	−	0.411541i	−0.825796	+	0.563969i	$0.809274\pi$
$410$	−11.0865	+	0.573835i	−0.547526	+	0.0283397i
$411$	0.736701	−	2.29204i	0.0363388	−	0.113058i
$412$	7.57753	+	23.1177i	0.373318	+	1.13893i
$413$	−4.43516	+	20.4750i	−0.218240	+	1.00751i
$414$	−24.8177	+	50.0447i	−1.21972	+	2.45956i
$415$	1.97048	−	14.4265i	0.0967272	−	0.708169i
$416$	25.4879	+	68.6435i	1.24965	+	3.36553i
$417$	1.71874	−	8.16141i	0.0841670	−	0.399666i
$418$	0.0753676	+	1.05815i	0.00368635	+	0.0517556i
$419$	−0.623494	+	13.7697i	−0.0304597	+	0.672693i	0.925421	+	0.378940i	$0.123711\pi$
$419$	−0.623494	+	13.7697i	−0.0304597	+	0.672693i	−0.955881	+	0.293754i	$0.905095\pi$
$420$	−24.8601	−	24.1034i	−1.21305	−	1.17613i
$421$	1.15501	−	0.871534i	0.0562917	−	0.0424759i	−0.573811	−	0.818988i	$-0.694536\pi$
$421$	1.15501	−	0.871534i	0.0562917	−	0.0424759i	0.630102	+	0.776512i	$0.283013\pi$
$422$	24.9534	−	36.3830i	1.21471	−	1.77110i
$423$	2.63462	−	6.30644i	0.128100	−	0.306630i
$424$	−10.9646	+	10.7540i	−0.532488	+	0.522260i
$425$	1.23943	+	2.02403i	0.0601210	+	0.0981798i
$426$	−38.6461	+	42.5271i	−1.87241	+	2.06045i
$427$	−22.6246	−	27.3197i	−1.09488	−	1.32209i
$428$	1.44232	+	44.6093i	0.0697170	+	2.15627i
$429$	0.449723	+	0.0736429i	0.0217128	+	0.00355551i
$430$	−35.6262	+	3.69790i	−1.71805	+	0.178329i
$431$	35.1323	−	8.32650i	1.69226	−	0.401073i	0.732251	−	0.681035i	$-0.238470\pi$
$431$	35.1323	−	8.32650i	1.69226	−	0.401073i	0.960011	+	0.279962i	$0.0903218\pi$
$432$	−16.2869	+	64.3862i	−0.783604	+	3.09778i
$433$	24.2681	+	5.75164i	1.16625	+	0.276406i	0.767742	−	0.640759i	$-0.221380\pi$
$433$	24.2681	+	5.75164i	1.16625	+	0.276406i	0.398508	+	0.917165i	$0.369528\pi$
$434$	−10.8865	−	1.41535i	−0.522571	−	0.0679388i
$435$	4.52944	+	21.6598i	0.217170	+	1.03851i
$436$	−5.24623	+	62.2826i	−0.251249	+	2.98279i
$437$	−42.8739	+	12.5342i	−2.05094	+	0.599592i
$438$	3.15777	+	13.3658i	0.150884	+	0.638641i
$439$	−27.7036	+	7.32726i	−1.32222	+	0.349711i	−0.847673	−	0.530519i	$-0.821997\pi$
$439$	−27.7036	+	7.32726i	−1.32222	+	0.349711i	−0.474547	+	0.880230i	$0.657388\pi$
$440$	−0.578444	−	0.662824i	−0.0275763	−	0.0315989i
$441$	−3.15793	−	3.92657i	−0.150378	−	0.186979i
$442$	0.237024	−	12.2209i	0.0112741	−	0.581290i
$443$	2.62699	−	23.8091i	0.124812	−	1.13120i	−0.754948	−	0.655785i	$-0.772338\pi$
$443$	2.62699	−	23.8091i	0.124812	−	1.13120i	0.879760	−	0.475419i	$-0.157703\pi$
$444$	23.1139	−	78.8554i	1.09694	−	3.74231i
$445$	−10.9205	−	8.92538i	−0.517682	−	0.423104i
$446$	3.41020	−	2.93745i	0.161477	−	0.139092i
$447$	5.59016	+	30.6697i	0.264405	+	1.45063i
$448$	−20.6905	+	41.8709i	−0.977536	+	1.97822i
$449$	14.4299	−	16.5348i	0.680987	−	0.780324i	−0.304052	−	0.952655i	$-0.598340\pi$
$449$	14.4299	−	16.5348i	0.680987	−	0.780324i	0.985039	+	0.172331i	$0.0551299\pi$
$450$	−13.3502	−	12.1491i	−0.629334	−	0.572714i
$451$	0.150579	+	0.0235502i	0.00709050	+	0.00110893i
$452$	16.7789	−	11.6681i	0.789214	−	0.548821i
$453$	6.14422	−	4.56746i	0.288681	−	0.214598i
$454$	28.5447	+	57.7652i	1.33967	+	2.71106i
$455$	−15.9078	−	4.20743i	−0.745771	−	0.197247i
$456$	−84.7885	+	45.9943i	−3.97059	+	2.15388i
$457$	7.49295	+	3.88521i	0.350506	+	0.181742i	0.626509	−	0.779414i	$-0.284483\pi$
$457$	7.49295	+	3.88521i	0.350506	+	0.181742i	−0.276003	+	0.961157i	$0.589010\pi$
$458$	−44.6354	−	59.9557i	−2.08567	−	2.80155i
$459$	3.21126	−	4.47272i	0.149889	−	0.208769i
$460$	35.8739	−	48.1870i	1.67263	−	2.24673i
$461$	−19.6225	+	9.53917i	−0.913913	+	0.444284i	−0.833526	−	0.552480i	$-0.813681\pi$
$461$	−19.6225	+	9.53917i	−0.913913	+	0.444284i	−0.0803871	+	0.996764i	$0.525616\pi$
$462$	0.368065	+	0.544989i	0.0171239	+	0.0253552i
$463$	−0.172921	+	0.0362885i	−0.00803634	+	0.00168647i	−0.209398	−	0.977830i	$-0.567151\pi$
$463$	−0.172921	+	0.0362885i	−0.00803634	+	0.00168647i	0.201362	+	0.979517i	$0.435463\pi$
$464$	85.4343	−	48.5919i	3.96619	−	2.25582i
$465$	5.07395	+	0.497152i	0.235299	+	0.0230549i
$466$	−4.65070	−	22.8968i	−0.215440	−	1.06067i
$467$	−1.38391	+	0.107566i	−0.0640396	+	0.00497755i	−0.109472	−	0.993990i	$-0.534916\pi$
$467$	−1.38391	+	0.107566i	−0.0640396	+	0.00497755i	0.0454326	+	0.998967i	$0.485533\pi$
$468$	17.5109	+	64.8793i	0.809441	+	2.99905i
$469$	1.28062	+	13.1660i	0.0591337	+	0.607948i
$470$	−5.53245	+	8.53129i	−0.255193	+	0.393519i
$471$	6.35008	+	1.20919i	0.292596	+	0.0557164i
$472$	−77.8336	+	10.1190i	−3.58258	+	0.465767i
$473$	0.489108	+	0.0507681i	0.0224892	+	0.00233432i
$474$	50.6140	+	13.7759i	2.32478	+	0.632747i
$475$	−0.0933044	−	14.4339i	−0.00428110	−	0.662271i
$476$	9.44257	−	8.56867i	0.432799	−	0.392745i
$477$	−4.13301	+	3.36819i	−0.189237	+	0.154219i
$478$	−22.0475	−	41.8561i	−1.00843	−	1.91446i
$479$	−25.8955	−	32.9686i	−1.18319	−	1.50638i	−0.817780	−	0.575530i	$-0.804796\pi$
$479$	−25.8955	−	32.9686i	−1.18319	−	1.50638i	−0.365414	−	0.930845i	$-0.619073\pi$
$480$	20.3380	−	44.6587i	0.928297	−	2.03838i
$481$	−8.75960	−	38.0542i	−0.399403	−	1.73512i
$482$	22.8306	−	37.2831i	1.03990	−	1.69820i
$483$	−19.1468	+	20.0051i	−0.871210	+	0.910263i
$484$	−28.0380	−	50.0464i	−1.27445	−	2.27484i
$485$	−12.9394	+	22.4117i	−0.587548	+	1.01766i
$486$	−13.9525	+	39.4843i	−0.632896	+	1.79105i
$487$	10.2666	+	17.7823i	0.465225	+	0.805793i	0.999212	−	0.0396995i	$-0.0126401\pi$
$487$	10.2666	+	17.7823i	0.465225	+	0.805793i	−0.533987	+	0.845493i	$0.679307\pi$
$488$	67.9297	−	114.222i	3.07503	−	5.17057i
$489$	3.18848	+	4.34762i	0.144188	+	0.196606i
$490$	3.57916	+	6.58692i	0.161690	+	0.297567i
$491$	−7.40428	+	6.89566i	−0.334151	+	0.311197i	−0.830601	−	0.556868i	$-0.812003\pi$
$491$	−7.40428	+	6.89566i	−0.334151	+	0.311197i	0.496450	+	0.868065i	$0.334637\pi$
$492$	6.01183	+	21.6558i	0.271034	+	0.976321i
$493$	−8.06624	+	1.15491i	−0.363285	+	0.0520147i
$494$	−39.6375	+	62.8891i	−1.78337	+	2.82951i
$495$	−0.178843	−	0.247563i	−0.00803841	−	0.0111271i
$496$	−4.79396	−	22.1314i	−0.215255	−	0.993729i
$497$	−24.5770	+	14.4022i	−1.10243	+	0.646026i
$498$	−40.6373	+	3.39407i	−1.82100	+	0.152092i
$499$	23.7485	−	32.7760i	1.06313	−	1.46726i	0.188740	−	0.982027i	$-0.439560\pi$
$499$	23.7485	−	32.7760i	1.06313	−	1.46726i	0.874388	−	0.485228i	$-0.161263\pi$
$500$	38.1183	+	49.8432i	1.70470	+	2.22906i
$501$	19.8075	+	11.7988i	0.884934	+	0.527134i
$502$	26.6935	+	52.3054i	1.19139	+	2.33450i
$503$	24.4034	−	17.4425i	1.08809	−	0.777722i	0.111703	−	0.993742i	$-0.464369\pi$
$503$	24.4034	−	17.4425i	1.08809	−	0.777722i	0.976389	+	0.216020i	$0.0693076\pi$
$504$	−31.3001	+	50.9523i	−1.39422	+	2.26960i
$505$	−2.74220	+	5.73482i	−0.122026	+	0.255196i
$506$	−0.854761	+	0.755736i	−0.0379988	+	0.0335966i
$507$	6.58970	+	6.72825i	0.292659	+	0.298812i
$508$	0.0970674	−	15.0160i	0.00430667	−	0.666226i
$509$	17.3855	+	19.4092i	0.770597	+	0.860297i	0.993416	−	0.114562i	$-0.0365466\pi$
$509$	17.3855	+	19.4092i	0.770597	+	0.860297i	−0.222819	+	0.974860i	$0.571526\pi$
$510$	−5.88924	+	5.69384i	−0.260780	+	0.252128i
$511$	−0.483690	+	6.79090i	−0.0213972	+	0.300412i
$512$	2.92570	+	0.341965i	0.129299	+	0.0151128i
$513$	−30.7761	+	13.1982i	−1.35880	+	0.582714i
$514$	74.0928	−	8.66020i	3.26809	−	0.381985i
$515$	−0.350459	−	7.73979i	−0.0154431	−	0.341056i
$516$	22.9823	+	68.7745i	1.01174	+	3.02763i
$517$	0.0983905	−	0.0990286i	0.00432721	−	0.00435527i
$518$	31.2695	−	46.8801i	1.37391	−	2.05980i
$519$	−3.89833	+	16.3967i	−0.171118	+	0.719736i
$520$	−5.17446	−	61.4305i	−0.226915	−	2.69391i
$521$	−6.89103	−	17.8482i	−0.301901	−	0.781944i	−0.997953	−	0.0639525i	$-0.979629\pi$
$521$	−6.89103	−	17.8482i	−0.301901	−	0.781944i	0.696051	−	0.717992i	$-0.254939\pi$
$522$	56.4547	−	25.5656i	2.47096	−	1.11898i
$523$	−9.51173	−	27.7991i	−0.415919	−	1.21557i	−0.933076	−	0.359679i	$-0.882886\pi$
$523$	−9.51173	−	27.7991i	−0.415919	−	1.21557i	0.517157	−	0.855890i	$-0.326990\pi$
$524$	69.8116	−	4.51905i	3.04973	−	0.197415i
$525$	−4.51861	−	7.72342i	−0.197208	−	0.337078i
$526$	−14.4803	−	76.3372i	−0.631370	−	3.32846i
$527$	−0.302073	+	1.85291i	−0.0131585	+	0.0807141i
$528$	−0.803770	+	1.09273i	−0.0349796	+	0.0475549i
$529$	−20.1830	−	14.8239i	−0.877524	−	0.644518i
$530$	6.94498	−	3.83208i	0.301671	−	0.166455i
$531$	−27.2287	+	1.01806i	−1.18163	+	0.0441799i
$532$	−76.0936	+	14.9443i	−3.29907	+	0.647917i
$533$	7.52761	+	7.57643i	0.326057	+	0.328171i
$534$	−17.7526	+	35.2861i	−0.768229	+	1.52698i
$535$	3.36735	−	13.8096i	0.145583	−	0.597040i
$536$	−44.8479	+	21.0896i	−1.93713	+	0.910934i
$537$	−2.42666	+	0.971154i	−0.104718	+	0.0419084i
$538$	42.3465	−	55.3721i	1.82569	−	2.38726i
$539$	−0.0295175	−	0.0985953i	−0.00127141	−	0.00424680i
$540$	22.3484	−	39.0998i	0.961721	−	1.68259i
$541$	−3.27932	+	10.9537i	−0.140989	+	0.470937i	−0.999095	−	0.0425364i	$-0.986456\pi$
$541$	−3.27932	+	10.9537i	−0.140989	+	0.470937i	0.858106	+	0.513473i	$0.171641\pi$
$542$	−0.390582	−	0.539054i	−0.0167769	−	0.0231544i
$543$	−5.61304	+	16.0285i	−0.240879	+	0.687851i
$544$	15.9330	+	8.52463i	0.683121	+	0.365491i
$545$	6.92882	−	18.6606i	0.296798	−	0.799331i
$546$	−1.81948	+	46.0483i	−0.0778665	+	1.97069i
$547$	23.0096	−	0.595086i	0.983820	−	0.0254440i	0.469403	−	0.882984i	$-0.344469\pi$
$547$	23.0096	−	0.595086i	0.983820	−	0.0254440i	0.514417	+	0.857540i	$0.328008\pi$
$548$	6.98568	+	1.94460i	0.298414	+	0.0830691i
$549$	27.1221	−	37.3209i	1.15754	−	1.59282i
$550$	−0.159045	−	0.332615i	−0.00678171	−	0.0141827i
$551$	45.6299	+	19.3339i	1.94390	+	0.823654i
$552$	−94.6914	−	42.3864i	−4.03033	−	1.80409i
$553$	21.9083	+	14.0069i	0.931634	+	0.595635i
$554$	−59.6725	+	40.3620i	−2.53524	+	1.71482i
$555$	−13.8261	+	22.2192i	−0.586886	+	0.943153i
$556$	24.7667	+	4.20216i	1.05034	+	0.178211i
$557$	−8.03467	+	3.28253i	−0.340440	+	0.139085i	−0.541971	−	0.840397i	$-0.682322\pi$
$557$	−8.03467	+	3.28253i	−0.340440	+	0.139085i	0.201531	+	0.979482i	$0.435408\pi$
$558$	−1.72923	−	14.1733i	−0.0732042	−	0.600005i
$559$	25.5182	+	23.1565i	1.07931	+	0.979417i
$560$	32.6802	−	36.4843i	1.38099	−	1.54174i
$561$	0.0951837	−	0.0598980i	0.00401866	−	0.00252890i
$562$	10.3731	−	20.3259i	0.437564	−	0.857396i
$563$	−1.95752	−	13.0692i	−0.0824998	−	0.550801i	−0.991098	−	0.133131i	$-0.957497\pi$
$563$	−1.95752	−	13.0692i	−0.0824998	−	0.550801i	0.908599	−	0.417670i	$-0.137153\pi$
$564$	19.2930	+	7.17916i	0.812382	+	0.302297i
$565$	−6.14438	+	2.14683i	−0.258496	+	0.0903177i
$566$	57.6362	−	48.3625i	2.42263	−	2.03283i
$567$	−12.4436	+	16.6164i	−0.522584	+	0.697824i
$568$	−81.7545	−	68.6002i	−3.43034	−	2.87840i
$569$	27.9345	+	10.5783i	1.17108	+	0.443465i	0.861672	−	0.507466i	$-0.169418\pi$
$569$	27.9345	+	10.5783i	1.17108	+	0.443465i	0.309405	+	0.950930i	$0.399870\pi$
$570$	48.5575	−	11.1412i	2.03385	−	0.466654i
$571$	5.17731	−	25.4895i	0.216664	−	1.06670i	−0.713809	−	0.700340i	$-0.753032\pi$
$571$	5.17731	−	25.4895i	0.216664	−	1.06670i	0.930473	−	0.366360i	$-0.119396\pi$
$572$	−0.168155	+	1.36223i	−0.00703091	+	0.0569577i
$573$	15.9859	+	13.9708i	0.667821	+	0.583637i
$574$	−0.498061	+	15.4045i	−0.0207887	+	0.642971i
$575$	12.2703	−	9.51018i	0.511706	−	0.396602i
$576$	−59.4316	−	12.5598i	−2.47632	−	0.523325i
$577$	5.53204	+	8.77717i	0.230302	+	0.365398i	0.941174	−	0.337923i	$-0.109724\pi$
$577$	5.53204	+	8.77717i	0.230302	+	0.365398i	−0.710872	+	0.703321i	$0.751700\pi$
$578$	27.6271	+	32.4958i	1.14914	+	1.35165i
$579$	5.96856	+	15.1980i	0.248045	+	0.631606i
$580$	−64.6481	+	16.2074i	−2.68436	+	0.672975i
$581$	−19.7286	−	4.40720i	−0.818482	−	0.182841i
$582$	69.1429	+	21.7316i	2.86606	+	0.900802i
$583$	−0.104119	+	0.0319061i	−0.00431219	+	0.00132142i
$584$	−24.5723	+	6.84017i	−1.01681	+	0.283048i
$585$	0.168591	−	21.4008i	0.00697036	−	0.884815i
$586$	2.86765	−	29.4820i	0.118461	−	1.21789i
$587$	26.6557	+	21.2170i	1.10020	+	0.875718i	0.992952	−	0.118514i	$-0.0378131\pi$
$587$	26.6557	+	21.2170i	1.10020	+	0.875718i	0.107247	+	0.994232i	$0.465797\pi$
$588$	11.4418	−	9.97096i	0.471851	−	0.411196i
$589$	7.39552	−	8.69882i	0.304727	−	0.358428i
$590$	40.1282	+	5.74549i	1.65205	+	0.236538i
$591$	−4.80857	−	37.1920i	−0.197798	−	1.52988i
$592$	112.748	+	28.2661i	4.63390	+	1.16173i
$593$	−15.3728	−	7.72052i	−0.631286	−	0.317044i	0.104228	−	0.994553i	$-0.466763\pi$
$593$	−15.3728	−	7.72052i	−0.631286	−	0.317044i	−0.735514	+	0.677510i	$0.763059\pi$
$594$	−0.567911	+	0.639588i	−0.0233017	+	0.0262426i
$595$	−3.62884	+	1.82247i	−0.148768	+	0.0747140i
$596$	−91.6381	+	20.4711i	−3.75364	+	0.838529i
$597$	−6.36191	−	13.5537i	−0.260376	−	0.554716i
$598$	−79.6253	+	7.22571i	−3.25612	+	0.295481i
$599$	0.211106	+	1.91331i	0.00862557	+	0.0781758i	0.997512	−	0.0704973i	$-0.0224586\pi$
$599$	0.211106	+	1.91331i	0.00862557	+	0.0781758i	−0.988886	+	0.148673i	$0.952500\pi$
$600$	21.5671	−	25.6658i	0.880472	−	1.04780i
$601$	41.0011	+	3.72070i	1.67247	+	0.151771i	0.885317	−	0.464988i	$-0.153941\pi$
$601$	41.0011	+	3.72070i	1.67247	+	0.151771i	0.787152	+	0.616759i	$0.211555\pi$
$602$	0.964276	+	49.7178i	0.0393009	+	2.02635i
$603$	−16.1755	+	5.86151i	−0.658716	+	0.238699i
$604$	14.4768	+	17.9484i	0.589051	+	0.730308i
$605$	4.32798	+	17.7491i	0.175957	+	0.721603i
$606$	17.3464	+	4.00584i	0.704650	+	0.162726i
$607$	−20.2272	+	36.1046i	−0.820997	+	1.46544i	0.0630343	+	0.998011i	$0.479922\pi$
$607$	−20.2272	+	36.1046i	−0.820997	+	1.46544i	−0.884031	+	0.467428i	$0.845181\pi$
$608$	−56.1745	−	94.4556i	−2.27818	−	3.83068i
$609$	30.4929	−	3.74219i	1.23564	−	0.151641i
$610$	−49.6191	+	47.4232i	−2.00902	+	1.92011i
$611$	9.66488	−	1.51156i	0.390999	−	0.0611512i
$612$	13.8428	+	9.13264i	0.559564	+	0.369165i
$613$	1.69164	−	1.02091i	0.0683245	−	0.0412341i	−0.482126	−	0.876102i	$-0.660135\pi$
$613$	1.69164	−	1.02091i	0.0683245	−	0.0412341i	0.550450	+	0.834868i	$0.314456\pi$
$614$	16.0707	−	22.7942i	0.648560	−	0.919898i
$615$	0.00505832	−	7.15757i	0.000203971	−	0.288621i
$616$	−0.984387	+	0.723006i	−0.0396621	+	0.0291308i
$617$	−8.12152	+	17.5646i	−0.326960	+	0.707126i	−0.999456	−	0.0329746i	$-0.989502\pi$
$617$	−8.12152	+	17.5646i	−0.326960	+	0.707126i	0.672496	+	0.740101i	$0.265222\pi$
$618$	−20.9451	+	5.66894i	−0.842534	+	0.228038i
$619$	5.52438	+	6.00928i	0.222044	+	0.241533i	0.837233	−	0.546846i	$-0.184172\pi$
$619$	5.52438	+	6.00928i	0.222044	+	0.241533i	−0.615190	+	0.788379i	$0.710921\pi$
$620$	−0.892844	+	15.3295i	−0.0358575	+	0.615649i
$621$	−31.3834	−	17.6697i	−1.25937	−	0.709061i
$622$	−0.183006	−	3.14209i	−0.00733786	−	0.125986i
$623$	−13.6204	+	14.0678i	−0.545688	+	0.563616i
$624$	−90.7246	+	28.3738i	−3.63189	+	1.13586i
$625$	−3.26974	−	8.15352i	−0.130789	−	0.326141i
$626$	−23.1512	−	64.9100i	−0.925310	−	2.59433i
$627$	−0.683844	+	0.0127797i	−0.0273101	+	0.000510371i
$628$	−2.88401	+	19.2548i	−0.115085	+	0.768351i
$629$	−7.83997	−	5.60367i	−0.312600	−	0.223433i
$630$	22.6307	−	21.0165i	0.901629	−	0.837317i
$631$	−25.9365	−	25.4384i	−1.03252	−	1.01269i	−0.999913	−	0.0132173i	$-0.995793\pi$
$631$	−25.9365	−	25.4384i	−1.03252	−	1.01269i	−0.0326045	−	0.999468i	$-0.510380\pi$
$632$	−21.8536	+	94.9382i	−0.869289	+	3.77644i
$633$	22.5826	+	17.2956i	0.897577	+	0.687439i
$634$	17.0080	+	54.2480i	0.675474	+	2.15446i
$635$	−1.31222	+	4.59869i	−0.0520739	+	0.182494i
$636$	−10.6283	−	12.0381i	−0.421439	−	0.477340i
$637$	2.42283	−	6.79298i	0.0959961	−	0.269148i
$638$	1.26485	−	0.0490821i	0.0500761	−	0.00194318i
$639$	−26.0760	−	26.3194i	−1.03155	−	1.04118i
$640$	31.2044	+	12.7484i	1.23346	+	0.503925i
$641$	−32.5035	−	20.1938i	−1.28381	−	0.797605i	−0.296290	−	0.955098i	$-0.595749\pi$
$641$	−32.5035	−	20.1938i	−1.28381	−	0.797605i	−0.987520	+	0.157493i	$0.949659\pi$
$642$	−39.8010	−	0.800078i	−1.57082	−	0.0315765i
$643$	11.5398	−	4.88956i	0.455086	−	0.192825i	−0.150493	−	0.988611i	$-0.548086\pi$
$643$	11.5398	−	4.88956i	0.455086	−	0.192825i	0.605578	+	0.795786i	$0.292942\pi$
$644$	−62.4836	−	55.2448i	−2.46220	−	2.17695i
$645$	−1.17740	−	23.0632i	−0.0463601	−	0.908112i
$646$	2.95181	+	18.1064i	0.116138	+	0.712385i
$647$	−10.8030	+	3.93196i	−0.424709	+	0.154581i	−0.545527	−	0.838093i	$-0.683670\pi$
$647$	−10.8030	+	3.93196i	−0.424709	+	0.154581i	0.120818	+	0.992675i	$0.461448\pi$
$648$	−74.2970	−	22.9974i	−2.91866	−	0.903422i
$649$	−0.522970	−	0.190346i	−0.0205284	−	0.00747172i
$650$	4.81490	−	25.3832i	0.188856	−	0.995611i
$651$	1.27906	−	6.96160i	0.0501302	−	0.272847i
$652$	−12.7053	+	10.1130i	−0.497578	+	0.396054i
$653$	1.74799	+	2.69548i	0.0684042	+	0.105482i	0.871565	−	0.490280i	$-0.163105\pi$
$653$	1.74799	+	2.69548i	0.0684042	+	0.105482i	−0.803161	+	0.595762i	$0.796850\pi$
$654$	−55.2299	−	7.58350i	−2.15966	−	0.296538i
$655$	−21.8045	−	4.57580i	−0.851973	−	0.178791i
$656$	−30.2733	+	9.70676i	−1.18198	+	0.378985i
$657$	−8.71236	+	1.58164i	−0.339902	+	0.0617055i
$658$	11.1579	+	8.64800i	0.434979	+	0.337134i
$659$	1.05787	−	1.27740i	0.0412089	−	0.0497605i	−0.749177	−	0.662370i	$-0.769551\pi$
$659$	1.05787	−	1.27740i	0.0412089	−	0.0497605i	0.790386	+	0.612609i	$0.209880\pi$
$660$	0.723791	−	0.567681i	0.0281735	−	0.0220970i
$661$	0.487441	+	0.236961i	0.0189593	+	0.00921673i	0.446664	−	0.894702i	$-0.352612\pi$
$661$	0.487441	+	0.236961i	0.0189593	+	0.00921673i	−0.427705	+	0.903918i	$0.640678\pi$
$662$	34.5750	−	17.9276i	1.34379	−	0.696777i
$663$	7.86055	+	0.565460i	0.305278	+	0.0219606i
$664$	−9.27839	−	75.1647i	−0.360071	−	2.91696i
$665$	24.6222	+	1.91379i	0.954809	+	0.0742136i
$666$	69.1564	+	24.2728i	2.67975	+	0.940550i
$667$	13.2951	+	51.6148i	0.514789	+	1.99853i
$668$	−33.1541	+	61.0152i	−1.28277	+	2.36075i
$669$	1.77610	+	2.29492i	0.0686681	+	0.0887268i
$670$	25.2354	−	4.28167i	0.974928	−	0.165415i
$671$	0.800410	−	0.497279i	0.0308995	−	0.0191972i
$672$	−59.4128	−	33.3406i	−2.29190	−	1.28614i
$673$	14.8309	−	33.1953i	0.571691	−	1.27958i	−0.365515	−	0.930805i	$-0.619107\pi$
$673$	14.8309	−	33.1953i	0.571691	−	1.27958i	0.937205	−	0.348778i	$-0.113403\pi$
$674$	−16.4335	−	17.4185i	−0.632996	−	0.670937i
$675$	8.27332	−	8.18523i	0.318440	−	0.315050i
$676$	−19.4656	+	20.6323i	−0.748675	+	0.793549i
$677$	8.23489	+	19.7903i	0.316492	+	0.760601i	0.999543	+	0.0302302i	$0.00962404\pi$
$677$	8.23489	+	19.7903i	0.316492	+	0.760601i	−0.683051	+	0.730371i	$0.739347\pi$
$678$	9.60864	+	15.4903i	0.369018	+	0.594901i
$679$	29.4975	+	20.5126i	1.13201	+	0.787202i
$680$	−10.9983	−	10.5116i	−0.421766	−	0.403101i
$681$	−38.1570	+	16.4274i	−1.46218	+	0.629497i
$682$	0.0763909	−	0.281453i	0.00292516	−	0.0107774i
$683$	−5.27237	+	15.4091i	−0.201742	+	0.589612i	−0.999918	−	0.0128116i	$-0.995922\pi$
$683$	−5.27237	+	15.4091i	−0.201742	+	0.589612i	0.798176	+	0.602424i	$0.205798\pi$
$684$	−43.3807	−	91.0535i	−1.65870	−	3.48152i
$685$	−1.97717	−	1.19323i	−0.0755436	−	0.0455908i
$686$	49.2456	−	21.6211i	1.88021	−	0.825498i
$687$	40.1109	−	26.7135i	1.53033	−	1.01918i
$688$	−95.9247	+	36.3249i	−3.65709	+	1.38487i
$689$	−7.20406	−	2.51708i	−0.274453	−	0.0958930i
$690$	41.2437	+	34.2048i	1.57012	+	1.30216i
$691$	0.297376	+	0.445833i	0.0113127	+	0.0169603i	0.837531	−	0.546389i	$-0.183998\pi$
$691$	0.297376	+	0.445833i	0.0113127	+	0.0169603i	−0.826219	+	0.563350i	$0.809512\pi$
$692$	−49.8107	−	9.78250i	−1.89352	−	0.371875i
$693$	−0.363330	+	0.218571i	−0.0138018	+	0.00830283i
$694$	−11.7566	+	14.5759i	−0.446276	+	0.553295i
$695$	−7.23968	−	3.40445i	−0.274617	−	0.129138i
$696$	51.5836	+	102.893i	1.95527	+	3.90013i
$697$	2.63019	+	0.170258i	0.0996256	+	0.00644897i
$698$	−18.4711	−	68.0546i	−0.699143	−	2.57591i
$699$	14.8994	−	2.22090i	0.563549	−	0.0840020i
$700$	22.7069	−	14.5175i	0.858239	−	0.548711i
$701$	−1.11784	+	2.59145i	−0.0422203	+	0.0978776i	−0.938021	−	0.346578i	$-0.887344\pi$
$701$	−1.11784	+	2.59145i	−0.0422203	+	0.0978776i	0.895801	+	0.444456i	$0.146603\pi$
$702$	−58.6063	+	12.5649i	−2.21195	+	0.474232i
$703$	23.2134	+	53.8147i	0.875509	+	2.02966i
$704$	−1.02769	−	0.695118i	−0.0387324	−	0.0261982i
$705$	−5.30606	−	3.85033i	−0.199838	−	0.145012i
$706$	−16.0834	+	49.0674i	−0.605305	+	1.84668i
$707$	7.61425	+	4.46197i	0.286364	+	0.167809i
$708$	−6.30184	−	81.8259i	−0.236837	−	3.07520i
$709$	31.1766	+	10.4427i	1.17086	+	0.392186i	0.835280	−	0.549825i	$-0.185306\pi$
$709$	31.1766	+	10.4427i	1.17086	+	0.392186i	0.335582	+	0.942011i	$0.391067\pi$
$710$	31.1761	+	45.4558i	1.17002	+	1.70593i
$711$	−10.5796	+	32.1229i	−0.396765	+	1.20470i
$712$	−66.7847	−	30.3574i	−2.50286	−	1.13769i
$713$	12.2636	+	0.634757i	0.459274	+	0.0237718i
$714$	7.19084	+	8.81094i	0.269110	+	0.329741i
$715$	0.167932	−	0.403578i	0.00628031	−	0.0150930i
$716$	−3.21133	−	7.18774i	−0.120013	−	0.268618i
$717$	27.6943	−	12.7815i	1.03426	−	0.477334i
$718$	−67.0850	−	38.1555i	−2.50359	−	1.42395i
$719$	−29.4040	−	9.42801i	−1.09658	−	0.351605i	−0.298657	−	0.954360i	$-0.596539\pi$
$719$	−29.4040	−	9.42801i	−1.09658	−	0.351605i	−0.797926	+	0.602755i	$0.794070\pi$
$720$	56.5131	+	29.4043i	2.10612	+	1.09583i
$721$	−10.7484	−	0.417087i	−0.400292	−	0.0155331i
$722$	22.5297	−	56.1807i	0.838468	−	2.09083i
$723$	23.2338	+	15.9592i	0.864076	+	0.593528i
$724$	−48.9066	−	14.9868i	−1.81760	−	0.556981i
$725$	−17.2175	−	0.445287i	−0.639441	−	0.0165375i
$726$	45.8867	−	22.6346i	1.70301	−	0.840048i
$727$	36.6531	+	0.473891i	1.35939	+	0.0175756i	0.689176	−	0.724594i	$-0.257973\pi$
$727$	36.6531	+	0.473891i	1.35939	+	0.0175756i	0.670212	+	0.742170i	$0.266203\pi$
$728$	−85.5887			−3.17213
$729$	−24.9510	−	10.3173i	−0.924112	−	0.382122i
$730$	13.1735			0.487574
$731$	8.50312	+	0.109938i	0.314499	+	0.00406619i
$732$	115.545	+	77.1879i	4.27067	+	2.85295i
$733$	26.7934	+	0.692944i	0.989637	+	0.0255945i	0.517283	−	0.855814i	$-0.326944\pi$
$733$	26.7934	+	0.692944i	0.989637	+	0.0255945i	0.472354	+	0.881409i	$0.343404\pi$
$734$	−51.4472	−	15.7654i	−1.89895	−	0.581910i
$735$	−4.36197	+	2.08196i	−0.160894	+	0.0767942i
$736$	43.9940	−	109.705i	1.62164	−	4.04377i
$737$	−0.351141	−	0.0136259i	−0.0129344	−	0.000501915i
$738$	−19.5698	+	4.34269i	−0.720375	+	0.159856i
$739$	24.1041	+	7.72868i	0.886685	+	0.284304i	0.713559	−	0.700596i	$-0.247082\pi$
$739$	24.1041	+	7.72868i	0.886685	+	0.284304i	0.173126	+	0.984900i	$0.444613\pi$
$740$	−68.5145	−	38.9685i	−2.51864	−	1.43251i
$741$	−39.1527	−	27.6455i	−1.43831	−	1.01558i
$742$	−4.49216	−	10.0546i	−0.164913	−	0.369115i
$743$	0.738665	−	1.77518i	0.0270990	−	0.0651249i	−0.909136	−	0.416499i	$-0.863257\pi$
$743$	0.738665	−	1.77518i	0.0270990	−	0.0651249i	0.936235	+	0.351375i	$0.114286\pi$
$744$	26.1757	−	4.24834i	0.959647	−	0.155752i
$745$	29.8634	+	1.54572i	1.09411	+	0.0566307i
$746$	21.2625	+	9.66500i	0.778476	+	0.353861i
$747$	−0.812488	−	26.2794i	−0.0297274	−	0.961511i
$748$	0.191586	+	0.279340i	0.00700509	+	0.0102137i
$749$	−18.7124	−	6.26780i	−0.683735	−	0.229020i
$750$	−46.1768	+	31.6226i	−1.68614	+	1.15469i
$751$	42.3895	+	24.8403i	1.54681	+	0.906435i	0.997489	+	0.0708267i	$0.0225637\pi$
$751$	42.3895	+	24.8403i	1.54681	+	0.906435i	0.549325	+	0.835609i	$0.314885\pi$
$752$	−9.06980	+	27.6703i	−0.330741	+	1.00903i
$753$	−34.5791	+	15.4199i	−1.26013	+	0.561932i
$754$	73.4734	+	49.6967i	2.67574	+	1.80985i
$755$	−2.90866	−	6.74304i	−0.105857	−	0.245404i
$756$	−51.4881	−	35.4741i	−1.87260	−	1.29018i
$757$	6.84568	−	15.8701i	0.248810	−	0.576807i	−0.747343	−	0.664439i	$-0.768671\pi$
$757$	6.84568	−	15.8701i	0.248810	−	0.576807i	0.996153	+	0.0876316i	$0.0279298\pi$
$758$	6.07451	−	3.88371i	0.220636	−	0.141063i
$759$	−0.457712	−	0.575877i	−0.0166139	−	0.0209030i
$760$	24.2361	+	89.2948i	0.879135	+	3.23906i
$761$	−22.1348	−	1.43283i	−0.802385	−	0.0519400i	−0.342046	−	0.939683i	$-0.611120\pi$
$761$	−22.1348	−	1.43283i	−0.802385	−	0.0519400i	−0.460339	+	0.887743i	$0.652272\pi$
$762$	13.3702	+	0.788207i	0.484351	+	0.0285537i
$763$	−25.0084	−	11.7602i	−0.905366	−	0.425747i
$764$	−40.1451	+	49.7721i	−1.45240	+	1.80069i
$765$	−3.46709	−	3.98419i	−0.125353	−	0.144049i
$766$	36.6822	+	7.20415i	1.32538	+	0.260297i
$767$	−21.6407	−	32.4444i	−0.781402	−	1.17150i
$768$	4.07564

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68619 - 0.0347299i) q^{2} +(0.113106 - 1.72835i) q^{3} +(5.21506 + 0.134874i) q^{4} +(-1.58849 - 0.486773i) q^{5} +(-0.363851 + 4.63875i) q^{6} +(-0.858532 + 2.14086i) q^{7} +(-8.63515 - 0.335083i) q^{8} +(-2.97441 - 0.390976i) q^{9} +O(q^{10})\)	\(q+(-2.68619 - 0.0347299i) q^{2} +(0.113106 - 1.72835i) q^{3} +(5.21506 + 0.134874i) q^{4} +(-1.58849 - 0.486773i) q^{5} +(-0.363851 + 4.63875i) q^{6} +(-0.858532 + 2.14086i) q^{7} +(-8.63515 - 0.335083i) q^{8} +(-2.97441 - 0.390976i) q^{9} +(4.25007 + 1.36273i) q^{10} +(-0.0532624 - 0.0302937i) q^{11} +(0.822967 - 8.99821i) q^{12} +(-1.75154 - 3.92038i) q^{13} +(2.38053 - 5.72094i) q^{14} +(-1.02098 + 2.69041i) q^{15} +(12.7643 + 0.660677i) q^{16} +(-0.964670 - 0.438496i) q^{17} +(7.97625 + 1.15354i) q^{18} +(3.64507 + 5.31464i) q^{19} +(-8.21841 - 2.75279i) q^{20} +(3.60306 + 1.72599i) q^{21} +(0.142021 + 0.0832243i) q^{22} +(-2.15891 + 6.58644i) q^{23} +(-1.55583 + 14.8867i) q^{24} +(-1.85522 - 1.25486i) q^{25} +(4.56882 + 10.5917i) q^{26} +(-1.01217 + 5.09662i) q^{27} +(-4.76604 + 11.0489i) q^{28} +(6.47881 - 4.14219i) q^{29} +(2.83599 - 7.19149i) q^{30} +(-0.464075 - 1.70983i) q^{31} +(-17.0172 - 1.10156i) q^{32} +(-0.0583825 + 0.0886299i) q^{33} +(2.57605 + 1.21139i) q^{34} +(2.40588 - 2.98282i) q^{35} +(-15.4590 - 2.44013i) q^{36} +(8.92374 + 1.75257i) q^{37} +(-9.60675 - 14.4027i) q^{38} +(-6.97392 + 2.58387i) q^{39} +(13.5537 + 4.73563i) q^{40} +(-2.32612 + 0.880858i) q^{41} +(-9.61855 - 4.76147i) q^{42} +(-7.34807 + 3.22614i) q^{43} +(-0.273681 - 0.165167i) q^{44} +(4.53451 + 2.06892i) q^{45} +(6.02797 - 17.6174i) q^{46} +(-0.596755 + 2.19867i) q^{47} +(2.58561 - 21.9866i) q^{48} +(1.21424 + 1.16051i) q^{49} +(4.93989 + 3.43521i) q^{50} +(-0.866987 + 1.61769i) q^{51} +(-8.60565 - 20.6813i) q^{52} +(1.21960 - 1.29270i) q^{53} +(2.89588 - 13.6553i) q^{54} +(0.0698606 + 0.0740479i) q^{55} +(8.13092 - 18.1990i) q^{56} +(9.59785 - 5.69884i) q^{57} +(-17.5471 + 10.9017i) q^{58} +(8.95461 - 1.51932i) q^{59} +(-5.68736 + 13.8930i) q^{60} +(-7.34231 + 13.5124i) q^{61} +(1.18721 + 4.60903i) q^{62} +(3.39065 - 6.03214i) q^{63} +(20.1872 + 1.56907i) q^{64} +(0.873972 + 7.08009i) q^{65} +(0.159904 - 0.236049i) q^{66} +(5.09120 - 2.63986i) q^{67} +(-4.97167 - 2.41689i) q^{68} +(11.1395 + 4.47632i) q^{69} +(-6.56624 + 7.92887i) q^{70} +(9.76121 + 7.56551i) q^{71} +(25.5535 + 4.37281i) q^{72} +(2.81064 - 0.901196i) q^{73} +(-23.9100 - 5.01764i) q^{74} +(-2.37867 + 3.06455i) q^{75} +(18.2924 + 28.2078i) q^{76} +(0.110582 - 0.0880193i) q^{77} +(18.8230 - 6.69855i) q^{78} +(2.10097 - 11.0759i) q^{79} +(-19.9544 - 7.26281i) q^{80} +(8.69428 + 2.32585i) q^{81} +(6.27899 - 2.28536i) q^{82} +(1.41014 + 8.64978i) q^{83} +(18.5574 + 9.48711i) q^{84} +(1.31892 + 1.16612i) q^{85} +(19.8503 - 8.41083i) q^{86} +(-6.42637 - 11.6662i) q^{87} +(0.449778 + 0.279438i) q^{88} +(7.85864 + 3.21061i) q^{89} +(-12.1087 - 5.71500i) q^{90} +(9.89676 - 0.384039i) q^{91} +(-12.1472 + 34.0575i) q^{92} +(-3.00767 + 0.608693i) q^{93} +(1.67936 - 5.88531i) q^{94} +(-3.20313 - 10.2166i) q^{95} +(-3.82864 + 29.2872i) q^{96} +(3.49414 - 15.1796i) q^{97} +(-3.22138 - 3.15951i) q^{98} +(0.146580 + 0.110930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

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