LMFDB - Embedded newform 729.2.e.s.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			649.2
Root			$-0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.s.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0300370 - 0.170348i) q^{2} +(1.85127 + 0.673807i) q^{4} +(-2.86237 + 2.40182i) q^{5} +(-2.84868 + 1.03683i) q^{7} +(0.343364 - 0.594724i) q^{8} +O(q^{10})$	\(q+(0.0300370 - 0.170348i) q^{2} +(1.85127 + 0.673807i) q^{4} +(-2.86237 + 2.40182i) q^{5} +(-2.84868 + 1.03683i) q^{7} +(0.343364 - 0.594724i) q^{8} +(0.323168 + 0.559743i) q^{10} +(-1.90875 - 1.60163i) q^{11} +(-0.132865 - 0.753515i) q^{13} +(0.0910570 + 0.516410i) q^{14} +(2.92734 + 2.45633i) q^{16} +(-2.31139 - 4.00345i) q^{17} +(0.305922 - 0.529872i) q^{19} +(-6.91738 + 2.51772i) q^{20} +(-0.330168 + 0.277044i) q^{22} +(-6.13091 - 2.23147i) q^{23} +(1.55622 - 8.82575i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(-1.13755 + 6.45137i) q^{29} +(-6.15539 - 2.24038i) q^{31} +(1.55849 - 1.30773i) q^{32} +(-0.751407 + 0.273490i) q^{34} +(5.66369 - 9.80980i) q^{35} +(-2.47984 - 4.29522i) q^{37} +(-0.0810738 - 0.0680290i) q^{38} +(0.445582 + 2.52702i) q^{40} +(0.913431 + 5.18032i) q^{41} +(4.26731 + 3.58070i) q^{43} +(-2.45442 - 4.25118i) q^{44} +(-0.564280 + 0.977362i) q^{46} +(-1.04082 + 0.378827i) q^{47} +(1.67762 - 1.40769i) q^{49} +(-1.45670 - 0.530197i) q^{50} +(0.261754 - 1.48448i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(-0.361503 + 2.05019i) q^{56} +(1.06481 + 0.387559i) q^{58} +(-9.07897 + 7.61816i) q^{59} +(-7.69327 + 2.80012i) q^{61} +(-0.566533 + 0.981264i) q^{62} +(3.64541 + 6.31404i) q^{64} +(2.19011 + 1.83772i) q^{65} +(-0.210520 - 1.19392i) q^{67} +(-1.58146 - 8.96889i) q^{68} +(-1.50096 - 1.25946i) q^{70} +(2.45973 + 4.26038i) q^{71} +(-2.14972 + 3.72343i) q^{73} +(-0.806169 + 0.293421i) q^{74} +(0.923375 - 0.774804i) q^{76} +(7.09803 + 2.58347i) q^{77} +(-2.04811 + 11.6154i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(1.56562 - 8.87910i) q^{83} +(16.2316 + 5.90782i) q^{85} +(0.738141 - 0.619374i) q^{86} +(-1.60792 + 0.585237i) q^{88} +(-3.76943 + 6.52884i) q^{89} +(1.15976 + 2.00876i) q^{91} +(-9.84638 - 8.26210i) q^{92} +(0.0332694 + 0.188680i) q^{94} +(0.396993 + 2.25146i) q^{95} +(-0.726481 - 0.609590i) q^{97} +(-0.189407 - 0.328062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.0300370	−	0.170348i	0.0212393	−	0.120454i	−0.972345	−	0.233550i	$-0.924966\pi$
$2$	0.0300370	−	0.170348i	0.0212393	−	0.120454i	0.993584	+	0.113096i	$0.0360768\pi$
$3$		0			0
$3$		0			0
$4$	1.85127	+	0.673807i	0.925635	+	0.336903i
$5$	−2.86237	+	2.40182i	−1.28009	+	1.07412i	−0.286861	+	0.957972i	$0.592612\pi$
$5$	−2.86237	+	2.40182i	−1.28009	+	1.07412i	−0.993231	+	0.116153i	$0.962944\pi$
$6$		0			0
$7$	−2.84868	+	1.03683i	−1.07670	+	0.391886i	−0.818678	−	0.574253i	$-0.805292\pi$
$7$	−2.84868	+	1.03683i	−1.07670	+	0.391886i	−0.258021	+	0.966139i	$0.583070\pi$
$8$	0.343364	−	0.594724i	0.121398	−	0.210267i
$9$		0			0
$10$	0.323168	+	0.559743i	0.102195	+	0.177006i
$11$	−1.90875	−	1.60163i	−0.575510	−	0.482910i	0.307959	−	0.951400i	$-0.400354\pi$
$11$	−1.90875	−	1.60163i	−0.575510	−	0.482910i	−0.883469	+	0.468490i	$0.844798\pi$
$12$		0			0
$13$	−0.132865	−	0.753515i	−0.0368501	−	0.208987i	0.960823	−	0.277162i	$-0.0893937\pi$
$13$	−0.132865	−	0.753515i	−0.0368501	−	0.208987i	−0.997673	+	0.0681742i	$0.978283\pi$
$14$	0.0910570	+	0.516410i	0.0243360	+	0.138016i
$15$		0			0
$16$	2.92734	+	2.45633i	0.731835	+	0.614083i
$17$	−2.31139	−	4.00345i	−0.560595	−	0.970979i	−0.997445	−	0.0714442i	$-0.977239\pi$
$17$	−2.31139	−	4.00345i	−0.560595	−	0.970979i	0.436850	−	0.899534i	$-0.356094\pi$
$18$		0			0
$19$	0.305922	−	0.529872i	0.0701833	−	0.121561i	−0.828798	−	0.559548i	$-0.810975\pi$
$19$	0.305922	−	0.529872i	0.0701833	−	0.121561i	0.898982	+	0.437987i	$0.144308\pi$
$20$	−6.91738	+	2.51772i	−1.54677	+	0.562980i
$21$		0			0
$22$	−0.330168	+	0.277044i	−0.0703920	+	0.0590659i
$23$	−6.13091	−	2.23147i	−1.27838	−	0.465293i	−0.388486	−	0.921455i	$-0.627002\pi$
$23$	−6.13091	−	2.23147i	−1.27838	−	0.465293i	−0.889897	+	0.456161i	$0.849224\pi$
$24$		0			0
$25$	1.55622	−	8.82575i	0.311244	−	1.76515i
$26$	−0.132351			−0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	−1.13755	+	6.45137i	−0.211238	+	1.19799i	0.676079	+	0.736829i	$0.263678\pi$
$29$	−1.13755	+	6.45137i	−0.211238	+	1.19799i	−0.887317	+	0.461160i	$0.847433\pi$
$30$		0			0
$31$	−6.15539	−	2.24038i	−1.10554	−	0.402384i	−0.276184	−	0.961105i	$-0.589070\pi$
$31$	−6.15539	−	2.24038i	−1.10554	−	0.402384i	−0.829356	+	0.558721i	$0.811292\pi$
$32$	1.55849	−	1.30773i	0.275504	−	0.231176i
$33$		0			0
$34$	−0.751407	+	0.273490i	−0.128865	+	0.0469031i
$35$	5.66369	−	9.80980i	0.957338	−	1.65816i
$36$		0			0
$37$	−2.47984	−	4.29522i	−0.407684	−	0.706129i	0.586946	−	0.809626i	$-0.300330\pi$
$37$	−2.47984	−	4.29522i	−0.407684	−	0.706129i	−0.994630	+	0.103497i	$0.966997\pi$
$38$	−0.0810738	−	0.0680290i	−0.0131519	−	0.0110358i
$39$		0			0
$40$	0.445582	+	2.52702i	0.0704527	+	0.399557i
$41$	0.913431	+	5.18032i	0.142654	+	0.809031i	0.969221	+	0.246192i	$0.0791795\pi$
$41$	0.913431	+	5.18032i	0.142654	+	0.809031i	−0.826567	+	0.562838i	$0.809709\pi$
$42$		0			0
$43$	4.26731	+	3.58070i	0.650758	+	0.546051i	0.907301	−	0.420482i	$-0.138139\pi$
$43$	4.26731	+	3.58070i	0.650758	+	0.546051i	−0.256543	+	0.966533i	$0.582583\pi$
$44$	−2.45442	−	4.25118i	−0.370018	−	0.640889i
$45$		0			0
$46$	−0.564280	+	0.977362i	−0.0831986	+	0.144104i
$47$	−1.04082	+	0.378827i	−0.151819	+	0.0552576i	−0.416812	−	0.908993i	$-0.636853\pi$
$47$	−1.04082	+	0.378827i	−0.151819	+	0.0552576i	0.264993	+	0.964250i	$0.414630\pi$
$48$		0			0
$49$	1.67762	−	1.40769i	0.239660	−	0.201099i
$50$	−1.45670	−	0.530197i	−0.206009	−	0.0749812i
$51$		0			0
$52$	0.261754	−	1.48448i	0.0362988	−	0.205861i
$53$	8.84310			1.21469			0.607346	−	0.794437i	$-0.292234\pi$
$53$	8.84310			1.21469			0.607346	+	0.794437i	$0.292234\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	−0.361503	+	2.05019i	−0.0483079	+	0.273968i
$57$		0			0
$58$	1.06481	+	0.387559i	0.139816	+	0.0508890i
$59$	−9.07897	+	7.61816i	−1.18198	+	0.991800i	−0.182018	+	0.983295i	$0.558263\pi$
$59$	−9.07897	+	7.61816i	−1.18198	+	0.991800i	−0.999964	+	0.00850504i	$0.997293\pi$
$60$		0			0
$61$	−7.69327	+	2.80012i	−0.985022	+	0.358519i	−0.783791	−	0.621025i	$-0.786716\pi$
$61$	−7.69327	+	2.80012i	−0.985022	+	0.358519i	−0.201231	+	0.979544i	$0.564494\pi$
$62$	−0.566533	+	0.981264i	−0.0719498	+	0.124621i
$63$		0			0
$64$	3.64541	+	6.31404i	0.455677	+	0.789255i
$65$	2.19011	+	1.83772i	0.271650	+	0.227941i
$66$		0			0
$67$	−0.210520	−	1.19392i	−0.0257192	−	0.145861i	0.969244	−	0.246102i	$-0.0791497\pi$
$67$	−0.210520	−	1.19392i	−0.0257192	−	0.145861i	−0.994963	+	0.100241i	$0.968039\pi$
$68$	−1.58146	−	8.96889i	−0.191780	−	1.08764i
$69$		0			0
$70$	−1.50096	−	1.25946i	−0.179399	−	0.150534i
$71$	2.45973	+	4.26038i	0.291916	+	0.505614i	0.974263	−	0.225415i	$-0.0723738\pi$
$71$	2.45973	+	4.26038i	0.291916	+	0.505614i	−0.682346	+	0.731029i	$0.739040\pi$
$72$		0			0
$73$	−2.14972	+	3.72343i	−0.251606	+	0.435795i	−0.963968	−	0.266017i	$-0.914292\pi$
$73$	−2.14972	+	3.72343i	−0.251606	+	0.435795i	0.712362	+	0.701812i	$0.247625\pi$
$74$	−0.806169	+	0.293421i	−0.0937152	+	0.0341095i
$75$		0			0
$76$	0.923375	−	0.774804i	0.105918	−	0.0888761i
$77$	7.09803	+	2.58347i	0.808896	+	0.294414i
$78$		0			0
$79$	−2.04811	+	11.6154i	−0.230431	+	1.30684i	0.621596	+	0.783338i	$0.286485\pi$
$79$	−2.04811	+	11.6154i	−0.230431	+	1.30684i	−0.852027	+	0.523499i	$0.824627\pi$
$80$	−14.2788			−1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	1.56562	−	8.87910i	0.171850	−	0.974608i	−0.769868	−	0.638203i	$-0.779678\pi$
$83$	1.56562	−	8.87910i	0.171850	−	0.974608i	0.941718	−	0.336404i	$-0.109211\pi$
$84$		0			0
$85$	16.2316	+	5.90782i	1.76057	+	0.640793i
$86$	0.738141	−	0.619374i	0.0795958	−	0.0667888i
$87$		0			0
$88$	−1.60792	+	0.585237i	−0.171405	+	0.0623865i
$89$	−3.76943	+	6.52884i	−0.399558	+	0.692055i	−0.993671	−	0.112326i	$-0.964170\pi$
$89$	−3.76943	+	6.52884i	−0.399558	+	0.692055i	0.594113	+	0.804382i	$0.297503\pi$
$90$		0			0
$91$	1.15976	+	2.00876i	0.121576	+	0.210575i
$92$	−9.84638	−	8.26210i	−1.02656	−	0.861383i
$93$		0			0
$94$	0.0332694	+	0.188680i	0.00343148	+	0.0194609i
$95$	0.396993	+	2.25146i	0.0407306	+	0.230995i
$96$		0			0
$97$	−0.726481	−	0.609590i	−0.0737630	−	0.0618945i	0.605161	−	0.796103i	$-0.293109\pi$
$97$	−0.726481	−	0.609590i	−0.0737630	−	0.0618945i	−0.678924	+	0.734209i	$0.737553\pi$
$98$	−0.189407	−	0.328062i	−0.0191330	−	0.0331393i
$99$		0			0
$100$	8.82783	−	15.2902i	0.882783	−	1.52902i
$101$	5.26994	−	1.91810i	0.524379	−	0.190858i	−0.0662479	−	0.997803i	$-0.521103\pi$
$101$	5.26994	−	1.91810i	0.524379	−	0.190858i	0.590627	+	0.806945i	$0.298881\pi$
$102$		0			0
$103$	−7.21998	+	6.05829i	−0.711406	+	0.596941i	−0.924993	−	0.379983i	$-0.875930\pi$
$103$	−7.21998	+	6.05829i	−0.711406	+	0.596941i	0.213587	+	0.976924i	$0.431485\pi$
$104$	−0.493754	−	0.179712i	−0.0484166	−	0.0176222i
$105$		0			0
$106$	0.265620	−	1.50640i	0.0257993	−	0.146315i
$107$	−1.27825			−0.123573			−0.0617864	−	0.998089i	$-0.519680\pi$
$107$	−1.27825			−0.123573			−0.0617864	+	0.998089i	$0.519680\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	0.279655	−	1.58600i	0.0266641	−	0.151220i
$111$		0			0
$112$	−10.8858	−	3.96212i	−1.02862	−	0.374386i
$113$	7.16402	−	6.01133i	0.673934	−	0.565498i	−0.240293	−	0.970700i	$-0.577243\pi$
$113$	7.16402	−	6.01133i	0.673934	−	0.565498i	0.914227	+	0.405203i	$0.132799\pi$
$114$		0			0
$115$	22.9085	−	8.33802i	2.13623	−	0.777524i
$116$	−6.45289	+	11.1767i	−0.599136	+	1.03773i
$117$		0			0
$118$	1.02503	+	1.77541i	0.0943621	+	0.163440i
$119$	10.7353	+	9.00800i	0.984105	+	0.825762i
$120$		0			0
$121$	−0.832027	−	4.71866i	−0.0756388	−	0.428969i
$122$	0.245913	+	1.39464i	0.0222639	+	0.126265i
$123$		0			0
$124$	−9.88569	−	8.29508i	−0.887762	−	0.744920i
$125$	7.40194	+	12.8205i	0.662050	+	1.14670i
$126$		0			0
$127$	−10.3984	+	18.0106i	−0.922710	+	1.59818i	−0.127505	+	0.991838i	$0.540697\pi$
$127$	−10.3984	+	18.0106i	−0.922710	+	1.59818i	−0.795204	+	0.606342i	$0.792636\pi$
$128$	5.00862	−	1.82299i	0.442704	−	0.161131i
$129$		0			0
$130$	0.378837	−	0.317882i	0.0332262	−	0.0278801i
$131$	0.616278	+	0.224307i	0.0538445	+	0.0195978i	0.368802	−	0.929508i	$-0.379768\pi$
$131$	0.616278	+	0.224307i	0.0538445	+	0.0195978i	−0.314958	+	0.949106i	$0.601990\pi$
$132$		0			0
$133$	−0.322083	+	1.82662i	−0.0279282	+	0.158388i
$134$	−0.209705			−0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	1.49122	−	8.45714i	0.127404	−	0.722542i	−0.852447	−	0.522813i	$-0.824883\pi$
$137$	1.49122	−	8.45714i	0.127404	−	0.722542i	0.979851	−	0.199729i	$-0.0640063\pi$
$138$		0			0
$139$	−12.6352	−	4.59885i	−1.07171	−	0.390069i	−0.254892	−	0.966969i	$-0.582040\pi$
$139$	−12.6352	−	4.59885i	−1.07171	−	0.390069i	−0.816815	+	0.576900i	$0.804262\pi$
$140$	17.0949	−	14.3443i	1.44478	−	1.21232i
$141$		0			0
$142$	0.799630	−	0.291042i	0.0671035	−	0.0244237i
$143$	−0.953247	+	1.65107i	−0.0797145	+	0.138070i
$144$		0			0
$145$	−12.2389	−	21.1984i	−1.01639	−	1.76043i
$146$	0.569708	+	0.478042i	0.0471494	+	0.0395630i
$147$		0			0
$148$	−1.69671	−	9.62254i	−0.139469	−	0.790968i
$149$	1.67085	+	9.47589i	0.136882	+	0.776295i	0.973531	+	0.228556i	$0.0734003\pi$
$149$	1.67085	+	9.47589i	0.136882	+	0.776295i	−0.836649	+	0.547739i	$0.815489\pi$
$150$		0			0
$151$	−5.46052	−	4.58192i	−0.444371	−	0.372871i	0.392971	−	0.919551i	$-0.371447\pi$
$151$	−5.46052	−	4.58192i	−0.444371	−	0.372871i	−0.837342	+	0.546679i	$0.815892\pi$
$152$	−0.210085	−	0.363878i	−0.0170402	−	0.0295144i
$153$		0			0
$154$	0.653293	−	1.13154i	0.0526439	−	0.0911818i
$155$	23.0000	−	8.37131i	1.84740	−	0.672400i
$156$		0			0
$157$	5.88764	−	4.94032i	0.469885	−	0.394280i	−0.376868	−	0.926267i	$-0.622999\pi$
$157$	5.88764	−	4.94032i	0.469885	−	0.394280i	0.846753	+	0.531987i	$0.178554\pi$
$158$	1.91714	+	0.697784i	0.152520	+	0.0555127i
$159$		0			0
$160$	−1.32005	+	7.48640i	−0.104360	+	0.591852i
$161$	19.7786			1.55877
$162$		0			0
$163$	1.04750			0.0820465			0.0410232	−	0.999158i	$-0.486938\pi$
$163$	1.04750			0.0820465			0.0410232	+	0.999158i	$0.486938\pi$
$164$	−1.79953	+	10.2056i	−0.140520	+	0.796927i
$165$		0			0
$166$	−1.46551	−	0.533402i	−0.113746	−	0.0414000i
$167$	6.39959	−	5.36990i	0.495215	−	0.415535i	−0.360676	−	0.932691i	$-0.617454\pi$
$167$	6.39959	−	5.36990i	0.495215	−	0.415535i	0.855891	+	0.517156i	$0.173009\pi$
$168$		0			0
$169$	11.6659	−	4.24603i	0.897375	−	0.326618i
$170$	1.49393	−	2.58757i	0.114580	−	0.198458i
$171$		0			0
$172$	5.48724	+	9.50417i	0.418398	+	0.724686i
$173$	16.7348	+	14.0422i	1.27233	+	1.06761i	0.994254	+	0.107049i	$0.0341402\pi$
$173$	16.7348	+	14.0422i	1.27233	+	1.06761i	0.278073	+	0.960560i	$0.410304\pi$
$174$		0			0
$175$	4.71767	+	26.7552i	0.356622	+	2.02251i
$176$	−1.65343	−	9.37704i	−0.124632	−	0.706821i
$177$		0			0
$178$	0.998953	+	0.838221i	0.0748747	+	0.0628273i
$179$	4.54433	+	7.87101i	0.339659	+	0.588307i	0.984369	−	0.176121i	$-0.0563549\pi$
$179$	4.54433	+	7.87101i	0.339659	+	0.588307i	−0.644709	+	0.764428i	$0.723022\pi$
$180$		0			0
$181$	3.56539	−	6.17543i	0.265013	−	0.459016i	−0.702554	−	0.711630i	$-0.747957\pi$
$181$	3.56539	−	6.17543i	0.265013	−	0.459016i	0.967567	+	0.252614i	$0.0812904\pi$
$182$	0.377024	−	0.137225i	0.0279469	−	0.0101718i
$183$		0			0
$184$	−3.43224	+	2.87999i	−0.253028	+	0.212316i
$185$	17.4146	+	6.33838i	1.28034	+	0.466007i
$186$		0			0
$187$	−2.00018	+	11.3436i	−0.146268	+	0.829525i
$188$	−2.18209			−0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	2.07607	−	11.7740i	0.150219	−	0.851936i	−0.812808	−	0.582532i	$-0.802062\pi$
$191$	2.07607	−	11.7740i	0.150219	−	0.851936i	0.963027	−	0.269404i	$-0.0868268\pi$
$192$		0			0
$193$	8.33849	+	3.03496i	0.600218	+	0.218461i	0.624218	−	0.781251i	$-0.285418\pi$
$193$	8.33849	+	3.03496i	0.600218	+	0.218461i	−0.0239999	+	0.999712i	$0.507640\pi$
$194$	−0.125664	+	0.105444i	−0.00902214	+	0.00757047i
$195$		0			0
$196$	4.05424	−	1.47562i	0.289589	−	0.105402i
$197$	−3.69895	+	6.40677i	−0.263539	+	0.456464i	−0.967180	−	0.254093i	$-0.918223\pi$
$197$	−3.69895	+	6.40677i	−0.263539	+	0.456464i	0.703641	+	0.710556i	$0.251557\pi$
$198$		0			0
$199$	5.19187	+	8.99259i	0.368042	+	0.637468i	0.989259	−	0.146171i	$-0.0466948\pi$
$199$	5.19187	+	8.99259i	0.368042	+	0.637468i	−0.621217	+	0.783638i	$0.713362\pi$
$200$	−4.71454	−	3.95597i	−0.333368	−	0.279729i
$201$		0			0
$202$	−0.168452	−	0.955338i	−0.0118522	−	0.0672174i
$203$	−3.44848	−	19.5573i	−0.242036	−	1.37265i
$204$		0			0
$205$	−15.0568	−	12.6341i	−1.05161	−	0.882406i
$206$	0.815151	+	1.41188i	0.0567942	+	0.0983705i
$207$		0			0
$208$	1.46194	−	2.53215i	0.101367	−	0.175573i
$209$	−1.43259	+	0.521420i	−0.0990942	+	0.0360674i
$210$		0			0
$211$	15.9806	−	13.4093i	1.10015	−	0.923133i	0.102712	−	0.994711i	$-0.467248\pi$
$211$	15.9806	−	13.4093i	1.10015	−	0.923133i	0.997435	+	0.0715777i	$0.0228034\pi$
$212$	16.3710	+	5.95854i	1.12436	+	0.409234i
$213$		0			0
$214$	−0.0383946	+	0.217747i	−0.00262460	+	0.0148849i
$215$	−20.8148			−1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	−0.222480	+	1.26175i	−0.0150683	+	0.0854564i
$219$		0			0
$220$	17.2360	+	6.27340i	1.16205	+	0.422952i
$221$	−2.70955	+	2.27358i	−0.182264	+	0.152938i
$222$		0			0
$223$	−22.1565	+	8.06432i	−1.48371	+	0.540027i	−0.951786	−	0.306764i	$-0.900754\pi$
$223$	−22.1565	+	8.06432i	−1.48371	+	0.540027i	−0.531926	+	0.846791i	$0.678531\pi$
$224$	−3.08373	+	5.34118i	−0.206041	+	0.356873i
$225$		0			0
$226$	−0.808832	−	1.40094i	−0.0538027	−	0.0931890i
$227$	−8.03131	−	6.73907i	−0.533057	−	0.447288i	0.336099	−	0.941827i	$-0.390892\pi$
$227$	−8.03131	−	6.73907i	−0.533057	−	0.447288i	−0.869155	+	0.494539i	$0.835337\pi$
$228$		0			0
$229$	−2.41066	−	13.6715i	−0.159301	−	0.903439i	−0.954748	−	0.297416i	$-0.903875\pi$
$229$	−2.41066	−	13.6715i	−0.159301	−	0.903439i	0.795447	−	0.606023i	$-0.207236\pi$
$230$	−0.732263	−	4.15287i	−0.0482840	−	0.273832i
$231$		0			0
$232$	3.44619	+	2.89170i	0.226254	+	0.189849i
$233$	−3.79982	−	6.58149i	−0.248935	−	0.431167i	0.714296	−	0.699844i	$-0.246747\pi$
$233$	−3.79982	−	6.58149i	−0.248935	−	0.431167i	−0.963230	+	0.268676i	$0.913414\pi$
$234$		0			0
$235$	2.06934	−	3.58420i	0.134989	−	0.233807i
$236$	−21.9408	+	7.98579i	−1.42822	+	0.519831i
$237$		0			0
$238$	1.85695	−	1.55817i	0.120368	−	0.101001i
$239$	−15.5601	−	5.66340i	−1.00650	−	0.366335i	−0.214411	−	0.976744i	$-0.568783\pi$
$239$	−15.5601	−	5.66340i	−1.00650	−	0.366335i	−0.792087	+	0.610408i	$0.791005\pi$
$240$		0			0
$241$	−2.52111	+	14.2979i	−0.162399	+	0.921010i	0.789307	+	0.613999i	$0.210440\pi$
$241$	−2.52111	+	14.2979i	−0.162399	+	0.921010i	−0.951706	+	0.307011i	$0.900671\pi$
$242$	−0.828806			−0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	−1.42096	+	8.05867i	−0.0907819	+	0.514850i
$246$		0			0
$247$	−0.439913	−	0.160115i	−0.0279910	−	0.0101879i
$248$	−3.44595	+	2.89149i	−0.218818	+	0.183610i
$249$		0			0
$250$	2.40629	−	0.875816i	0.152187	−	0.0553915i
$251$	−4.52591	+	7.83910i	−0.285673	+	0.494800i	−0.972772	−	0.231764i	$-0.925550\pi$
$251$	−4.52591	+	7.83910i	−0.285673	+	0.494800i	0.687099	+	0.726563i	$0.258884\pi$
$252$		0			0
$253$	8.12838	+	14.0788i	0.511027	+	0.885125i
$254$	2.75573	+	2.31233i	0.172910	+	0.145089i
$255$		0			0
$256$	2.37198	+	13.4522i	0.148249	+	0.840760i
$257$	1.68437	+	9.55251i	0.105068	+	0.595870i	0.991193	+	0.132424i	$0.0422760\pi$
$257$	1.68437	+	9.55251i	0.105068	+	0.595870i	−0.886125	+	0.463446i	$0.846613\pi$
$258$		0			0
$259$	11.5177	+	9.66449i	0.715675	+	0.600522i
$260$	2.81622	+	4.87783i	0.174654	+	0.302510i
$261$		0			0
$262$	0.0567214	−	0.0982443i	0.00350426	−	0.00606955i
$263$	25.2357	−	9.18503i	1.55610	−	0.566373i	0.586260	−	0.810123i	$-0.300600\pi$
$263$	25.2357	−	9.18503i	1.55610	−	0.566373i	0.969838	+	0.243749i	$0.0783775\pi$
$264$		0			0
$265$	−25.3122	+	21.2395i	−1.55492	+	1.30473i
$266$	0.301488	+	0.109732i	0.0184854	+	0.00672813i
$267$		0			0
$268$	0.414742	−	2.35212i	0.0253344	−	0.143678i
$269$	11.7388			0.715729			0.357865	−	0.933774i	$-0.383505\pi$
$269$	11.7388			0.715729			0.357865	+	0.933774i	$0.383505\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	3.06756	−	17.3970i	0.185998	−	1.05485i
$273$		0			0
$274$	−1.39587	−	0.508053i	−0.0843273	−	0.0306926i
$275$	−17.1060	+	14.3537i	−1.03153	+	0.865558i
$276$		0			0
$277$	0.953248	−	0.346954i	0.0572751	−	0.0208464i	−0.313224	−	0.949679i	$-0.601409\pi$
$277$	0.953248	−	0.346954i	0.0572751	−	0.0208464i	0.370499	+	0.928833i	$0.379187\pi$
$278$	−1.16293	+	2.01425i	−0.0697479	+	0.120807i
$279$		0			0
$280$	−3.88942	−	6.73667i	−0.232437	−	0.402593i
$281$	−21.0888	−	17.6956i	−1.25805	−	1.05563i	−0.995887	−	0.0906075i	$-0.971119\pi$
$281$	−21.0888	−	17.6956i	−1.25805	−	1.05563i	−0.262165	−	0.965023i	$-0.584436\pi$
$282$		0			0
$283$	−4.65427	−	26.3957i	−0.276668	−	1.56906i	−0.733614	−	0.679566i	$-0.762168\pi$
$283$	−4.65427	−	26.3957i	−0.276668	−	1.56906i	0.456946	−	0.889494i	$-0.348943\pi$
$284$	1.68295	+	9.54449i	0.0998648	+	0.566361i
$285$		0			0
$286$	0.252624	+	0.211977i	0.0149380	+	0.0125345i
$287$	−7.97320	−	13.8100i	−0.470643	−	0.815178i
$288$		0			0
$289$	−2.18506	+	3.78464i	−0.128533	+	0.222626i
$290$	−3.97873	+	1.44814i	−0.233639	+	0.0850376i
$291$		0			0
$292$	−6.48859	+	5.44458i	−0.379716	+	0.318620i
$293$	−17.5321	−	6.38116i	−1.02424	−	0.372791i	−0.225352	−	0.974277i	$-0.572353\pi$
$293$	−17.5321	−	6.38116i	−1.02424	−	0.372791i	−0.798883	+	0.601486i	$0.794576\pi$
$294$		0			0
$295$	7.68998	−	43.6120i	0.447728	−	2.53919i
$296$	−3.40596			−0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	−0.866861	+	4.91621i	−0.0501319	+	0.284312i
$300$		0			0
$301$	−15.8688	−	5.77576i	−0.914660	−	0.332909i
$302$	−0.944539	+	0.792562i	−0.0543521	+	0.0456068i
$303$		0			0
$304$	2.19708	−	0.799671i	0.126011	−	0.0458643i
$305$	15.2956	−	26.4928i	0.875825	−	1.51697i
$306$		0			0
$307$	−16.8946	−	29.2624i	−0.964227	−	1.67009i	−0.711677	−	0.702507i	$-0.752064\pi$
$307$	−16.8946	−	29.2624i	−0.964227	−	1.67009i	−0.252551	−	0.967584i	$-0.581269\pi$
$308$	11.3996	+	9.56541i	0.649553	+	0.545040i
$309$		0			0
$310$	−0.735187	−	4.16945i	−0.0417558	−	0.236809i
$311$	6.02326	+	34.1596i	0.341548	+	1.93701i	0.349214	+	0.937043i	$0.386448\pi$
$311$	6.02326	+	34.1596i	0.341548	+	1.93701i	−0.00766664	+	0.999971i	$0.502440\pi$
$312$		0			0
$313$	2.55888	+	2.14716i	0.144636	+	0.121364i	0.712235	−	0.701941i	$-0.247683\pi$
$313$	2.55888	+	2.14716i	0.144636	+	0.121364i	−0.567599	+	0.823305i	$0.692127\pi$
$314$	−0.664726	−	1.15134i	−0.0375127	−	0.0649739i
$315$		0			0
$316$	−11.6182	+	20.1232i	−0.653572	+	1.13202i
$317$	−29.1613	+	10.6138i	−1.63786	+	0.596133i	−0.986663	−	0.162775i	$-0.947956\pi$
$317$	−29.1613	+	10.6138i	−1.63786	+	0.596133i	−0.651198	+	0.758908i	$0.725733\pi$
$318$		0			0
$319$	12.5040	−	10.4921i	0.700090	−	0.587446i
$320$	−25.5997	−	9.31753i	−1.43107	−	0.520866i
$321$		0			0
$322$	0.594090	−	3.36925i	0.0331073	−	0.187761i
$323$	−2.82842			−0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	0.0314637	−	0.178440i	0.00174261	−	0.00988285i
$327$		0			0
$328$	3.39450	+	1.23550i	0.187430	+	0.0682190i
$329$	2.57217	−	2.15831i	0.141809	−	0.118992i
$330$		0			0
$331$	−3.07437	+	1.11898i	−0.168983	+	0.0615047i	−0.425126	−	0.905134i	$-0.639770\pi$
$331$	−3.07437	+	1.11898i	−0.168983	+	0.0615047i	0.256143	+	0.966639i	$0.417548\pi$
$332$	8.88119	−	15.3827i	0.487419	−	0.844234i
$333$		0			0
$334$	−0.722527	−	1.25145i	−0.0395349	−	0.0684765i
$335$	3.47016	+	2.91181i	0.189595	+	0.159089i
$336$		0			0
$337$	1.10541	+	6.26910i	0.0602156	+	0.341500i	1.00000		0.000268386i	$-8.54299e-5\pi$
$337$	1.10541	+	6.26910i	0.0602156	+	0.341500i	−0.939784	+	0.341768i	$0.888974\pi$
$338$	−0.372896	−	2.11480i	−0.0202829	−	0.115030i
$339$		0			0
$340$	26.0683	+	21.8739i	1.41375	+	1.18628i
$341$	8.16083	+	14.1350i	0.441934	+	0.765452i
$342$		0			0
$343$	7.29078	−	12.6280i	0.393665	−	0.681848i
$344$	3.59477	−	1.30839i	0.193817	−	0.0705435i
$345$		0			0
$346$	2.89473	−	2.42896i	0.155621	−	0.130582i
$347$	−8.26216	−	3.00718i	−0.443536	−	0.161434i	0.110591	−	0.993866i	$-0.464726\pi$
$347$	−8.26216	−	3.00718i	−0.443536	−	0.161434i	−0.554127	+	0.832432i	$0.686948\pi$
$348$		0			0
$349$	2.50057	−	14.1815i	0.133853	−	0.759116i	−0.841799	−	0.539791i	$-0.818503\pi$
$349$	2.50057	−	14.1815i	0.133853	−	0.759116i	0.975652	−	0.219325i	$-0.0703855\pi$
$350$	4.69941			0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	−5.76520	+	32.6961i	−0.306851	+	1.74024i	0.307812	+	0.951447i	$0.400403\pi$
$353$	−5.76520	+	32.6961i	−0.306851	+	1.74024i	−0.614663	+	0.788790i	$0.710708\pi$
$354$		0			0
$355$	−17.2733	−	6.28697i	−0.916773	−	0.333678i
$356$	−11.3774	+	9.54677i	−0.603001	+	0.505978i
$357$		0			0
$358$	1.47731	−	0.537697i	0.0780782	−	0.0284182i
$359$	2.47257	−	4.28262i	0.130497	−	0.226028i	−0.793371	−	0.608738i	$-0.791676\pi$
$359$	2.47257	−	4.28262i	0.130497	−	0.226028i	0.923868	+	0.382710i	$0.125009\pi$
$360$		0			0
$361$	9.31282	+	16.1303i	0.490149	+	0.848962i
$362$	−0.944879	−	0.792848i	−0.0496617	−	0.0416711i
$363$		0			0
$364$	0.793508	+	4.50021i	0.0415911	+	0.235875i
$365$	−2.78969	−	15.8211i	−0.146019	−	0.828114i
$366$		0			0
$367$	−1.90933	−	1.60212i	−0.0996662	−	0.0836299i	0.591593	−	0.806237i	$-0.298499\pi$
$367$	−1.90933	−	1.60212i	−0.0996662	−	0.0836299i	−0.691259	+	0.722607i	$0.742944\pi$
$368$	−12.4660	−	21.5918i	−0.649837	−	1.12555i
$369$		0			0
$370$	1.60281	−	2.77615i	0.0833262	−	0.144325i
$371$	−25.1911	+	9.16882i	−1.30786	+	0.476021i
$372$		0			0
$373$	−21.4857	+	18.0286i	−1.11249	+	0.933487i	−0.998201	−	0.0599605i	$-0.980903\pi$
$373$	−21.4857	+	18.0286i	−1.11249	+	0.933487i	−0.114286	+	0.993448i	$0.536458\pi$
$374$	1.87228	+	0.681453i	0.0968131	+	0.0352371i
$375$		0			0
$376$	−0.132082	+	0.749075i	−0.00681162	+	0.0386306i
$377$	5.01234			0.258149
$378$		0			0
$379$	5.13991			0.264019			0.132010	−	0.991248i	$-0.457857\pi$
$379$	5.13991			0.264019			0.132010	+	0.991248i	$0.457857\pi$
$380$	−0.782108	+	4.43556i	−0.0401213	+	0.227539i
$381$		0			0
$382$	−1.94332	−	0.707310i	−0.0994288	−	0.0361891i
$383$	0.0342214	−	0.0287152i	0.00174863	−	0.00146728i	−0.641913	−	0.766778i	$-0.721859\pi$
$383$	0.0342214	−	0.0287152i	0.00174863	−	0.00146728i	0.643662	+	0.765310i	$0.277414\pi$
$384$		0			0
$385$	−26.5223	+	9.65331i	−1.35170	+	0.491978i
$386$	0.767463	−	1.32928i	0.0390628	−	0.0676588i
$387$		0			0
$388$	−0.934167	−	1.61802i	−0.0474251	−	0.0821427i
$389$	−16.0733	−	13.4871i	−0.814951	−	0.683825i	0.136833	−	0.990594i	$-0.456308\pi$
$389$	−16.0733	−	13.4871i	−0.814951	−	0.683825i	−0.951784	+	0.306769i	$0.900752\pi$
$390$		0			0
$391$	5.23736	+	29.7026i	0.264865	+	1.50212i
$392$	−0.261153	−	1.48107i	−0.0131902	−	0.0748054i
$393$		0			0
$394$	0.980276	+	0.822549i	0.0493856	+	0.0414394i
$395$	−22.0356	−	38.1668i	−1.10873	−	1.92038i
$396$		0			0
$397$	0.00122821	−	0.00212731i	6.16419e−5	−	0.000106767i	−0.865995	−	0.500053i	$-0.833314\pi$
$397$	0.00122821	−	0.00212731i	6.16419e−5	−	0.000106767i	0.866056	+	0.499947i	$0.166647\pi$
$398$	1.68782	−	0.614316i	0.0846027	−	0.0307929i
$399$		0			0
$400$	26.2345	−	22.0134i	1.31173	−	1.10067i
$401$	23.7332	+	8.63817i	1.18518	+	0.431370i	0.858028	−	0.513603i	$-0.171689\pi$
$401$	23.7332	+	8.63817i	1.18518	+	0.431370i	0.327150	+	0.944972i	$0.393912\pi$
$402$		0			0
$403$	−0.870322	+	4.93584i	−0.0433538	+	0.245872i
$404$	11.0485			0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	−2.14595	+	12.1703i	−0.106371	+	0.603259i
$408$		0			0
$409$	21.8841	+	7.96515i	1.08210	+	0.393851i	0.820688	−	0.571377i	$-0.193590\pi$
$409$	21.8841	+	7.96515i	1.08210	+	0.393851i	0.261410	+	0.965228i	$0.415813\pi$
$410$	−2.60446	+	2.18540i	−0.128625	+	0.107929i
$411$		0			0
$412$	−17.4482	+	6.35064i	−0.859613	+	0.312874i
$413$	17.9643	−	31.1151i	0.883965	−	1.53107i
$414$		0			0
$415$	16.8446	+	29.1756i	0.826867	+	1.43218i
$416$	−1.19246	−	1.00059i	−0.0584651	−	0.0490581i
$417$		0			0
$418$	0.0457922	+	0.259701i	0.00223977	+	0.0127024i
$419$	−5.43317	−	30.8130i	−0.265428	−	1.50531i	−0.767815	−	0.640672i	$-0.778656\pi$
$419$	−5.43317	−	30.8130i	−0.265428	−	1.50531i	0.502387	−	0.864643i	$-0.332455\pi$
$420$		0			0
$421$	23.3870	+	19.6240i	1.13981	+	0.956417i	0.999433	−	0.0336807i	$-0.0107229\pi$
$421$	23.3870	+	19.6240i	1.13981	+	0.956417i	0.140381	+	0.990098i	$0.455167\pi$
$422$	−1.80424	−	3.12503i	−0.0878289	−	0.152124i
$423$		0			0
$424$	3.03640	−	5.25920i	0.147461	−	0.255409i
$425$	−38.9304	+	14.1695i	−1.88840	+	0.687323i
$426$		0			0
$427$	19.0124	−	15.9533i	0.920073	−	0.772033i
$428$	−2.36638	−	0.861291i	−0.114383	−	0.0416321i
$429$		0			0
$430$	−0.625213	+	3.54576i	−0.0301505	+	0.170992i
$431$	−12.4246			−0.598474			−0.299237	−	0.954179i	$-0.596732\pi$
$431$	−12.4246			−0.598474			−0.299237	+	0.954179i	$0.596732\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	0.596462	−	3.38270i	0.0286311	−	0.162375i
$435$		0			0
$436$	−13.7121	−	4.99081i	−0.656692	−	0.239017i
$437$	−3.05797	+	2.56594i	−0.146283	+	0.122746i
$438$		0			0
$439$	−28.2935	+	10.2980i	−1.35038	+	0.491497i	−0.913065	−	0.407813i	$-0.866292\pi$
$439$	−28.2935	+	10.2980i	−1.35038	+	0.491497i	−0.437312	+	0.899310i	$0.644069\pi$
$440$	3.19685	−	5.53711i	0.152404	−	0.263971i
$441$		0			0
$442$	0.305914	+	0.529859i	0.0145508	+	0.0252028i
$443$	10.4654	+	8.78149i	0.497225	+	0.417221i	0.856607	−	0.515969i	$-0.172568\pi$
$443$	10.4654	+	8.78149i	0.497225	+	0.417221i	−0.359382	+	0.933191i	$0.617013\pi$
$444$		0			0
$445$	−4.89156	−	27.7414i	−0.231882	−	1.31507i
$446$	0.708226	+	4.01655i	0.0335355	+	0.190189i
$447$		0			0
$448$	−16.9312	−	14.2070i	−0.799925	−	0.671217i
$449$	10.9995	+	19.0516i	0.519097	+	0.899102i	0.999754	+	0.0221934i	$0.00706496\pi$
$449$	10.9995	+	19.0516i	0.519097	+	0.899102i	−0.480657	+	0.876909i	$0.659602\pi$
$450$		0			0
$451$	6.55346	−	11.3509i	0.308590	−	0.534494i
$452$	17.3130	−	6.30142i	0.814335	−	0.296394i
$453$		0			0
$454$	−1.38922	+	1.16570i	−0.0651995	+	0.0547089i
$455$	−8.14433	−	2.96429i	−0.381812	−	0.138968i
$456$		0			0
$457$	−0.258532	+	1.46621i	−0.0120936	+	0.0685863i	−0.990257	−	0.139250i	$-0.955531\pi$
$457$	−0.258532	+	1.46621i	−0.0120936	+	0.0685863i	0.978164	+	0.207836i	$0.0666420\pi$
$458$	−2.40132			−0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	−1.23522	+	7.00527i	−0.0575298	+	0.326268i	−0.999967	−	0.00811518i	$-0.997417\pi$
$461$	−1.23522	+	7.00527i	−0.0575298	+	0.326268i	0.942437	+	0.334383i	$0.108528\pi$
$462$		0			0
$463$	24.9401	+	9.07746i	1.15907	+	0.421866i	0.848764	−	0.528772i	$-0.177347\pi$
$463$	24.9401	+	9.07746i	1.15907	+	0.421866i	0.310302	+	0.950638i	$0.399570\pi$
$464$	−19.1767	+	16.0912i	−0.890256	+	0.747013i
$465$		0			0
$466$	−1.23528	+	0.449605i	−0.0572232	+	0.0208275i
$467$	−13.0760	+	22.6482i	−0.605084	+	1.04804i	0.386955	+	0.922099i	$0.373527\pi$
$467$	−13.0760	+	22.6482i	−0.605084	+	1.04804i	−0.992038	+	0.125937i	$0.959806\pi$
$468$		0			0
$469$	1.83760	+	3.18282i	0.0848525	+	0.146969i
$470$	−0.548405	−	0.460166i	−0.0252960	−	0.0212259i
$471$		0			0
$472$	1.41331	+	8.01529i	0.0650529	+	0.368933i
$473$	−2.41027	−	13.6693i	−0.110824	−	0.628515i
$474$		0			0
$475$	−4.20044	−	3.52459i	−0.192729	−	0.161719i
$476$	13.8043	+	23.9098i	0.632719	+	1.09590i
$477$		0			0
$478$	−1.43213	+	2.48052i	−0.0655040	+	0.113456i
$479$	9.77896	−	3.55925i	0.446812	−	0.162626i	−0.108808	−	0.994063i	$-0.534703\pi$
$479$	9.77896	−	3.55925i	0.446812	−	0.162626i	0.555620	+	0.831437i	$0.312481\pi$
$480$		0			0
$481$	−2.90702	+	2.43928i	−0.132549	+	0.111222i
$482$	2.35990	+	0.858932i	0.107490	+	0.0391233i
$483$		0			0
$484$	1.63916	−	9.29613i	0.0745072	−	0.422551i
$485$	3.54358			0.160906
$486$		0			0
$487$	−18.4664			−0.836791			−0.418396	−	0.908265i	$-0.637407\pi$
$487$	−18.4664			−0.836791			−0.418396	+	0.908265i	$0.637407\pi$
$488$	−0.976293	+	5.53683i	−0.0441947	+	0.250641i
$489$		0			0
$490$	1.33010	+	0.484116i	0.0600877	+	0.0218701i
$491$	−13.0028	+	10.9106i	−0.586806	+	0.492389i	−0.887174	−	0.461435i	$-0.847335\pi$
$491$	−13.0028	+	10.9106i	−0.586806	+	0.492389i	0.300368	+	0.953823i	$0.402890\pi$
$492$		0			0
$493$	28.4570	−	10.3575i	1.28164	−	0.466479i
$494$	−0.0404890	+	0.0701289i	−0.00182168	+	0.00315525i
$495$		0			0
$496$	−12.5158	−	21.6780i	−0.561976	−	0.973371i
$497$	−11.4243	−	9.58611i	−0.512449	−	0.429996i
$498$		0			0
$499$	4.27976	+	24.2717i	0.191589	+	1.08655i	0.917194	+	0.398441i	$0.130449\pi$
$499$	4.27976	+	24.2717i	0.191589	+	1.08655i	−0.725605	+	0.688111i	$0.758440\pi$
$500$	5.06442	+	28.7218i	0.226488	+	1.28448i
$501$		0			0
$502$	1.19943	+	1.00644i	0.0535332	+	0.0449197i
$503$	−20.0569	−	34.7395i	−0.894291	−	1.54896i	−0.834679	−	0.550736i	$-0.814347\pi$
$503$	−20.0569	−	34.7395i	−0.894291	−	1.54896i	−0.0596120	−	0.998222i	$-0.518986\pi$
$504$		0			0
$505$	−10.4776	+	18.1478i	−0.466248	+	0.807564i
$506$	2.64244	−	0.961770i	0.117471	−	0.0427559i
$507$		0			0
$508$	−31.3859	+	26.3359i	−1.39252	+	1.16847i
$509$	−4.65009	−	1.69249i	−0.206111	−	0.0750184i	0.236901	−	0.971534i	$-0.423868\pi$
$509$	−4.65009	−	1.69249i	−0.206111	−	0.0750184i	−0.443013	+	0.896515i	$0.646090\pi$
$510$		0			0
$511$	2.26329	−	12.8358i	0.100122	−	0.567821i
$512$	13.0229			0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	6.11540	−	34.6821i	0.269477	−	1.52828i
$516$		0			0
$517$	2.59340	+	0.943922i	0.114058	+	0.0415136i
$518$	1.99228	−	1.67172i	0.0875359	−	0.0734514i
$519$		0			0
$520$	1.84494	−	0.671505i	0.0809061	−	0.0294474i
$521$	−3.86979	+	6.70267i	−0.169539	+	0.293649i	−0.938258	−	0.345937i	$-0.887561\pi$
$521$	−3.86979	+	6.70267i	−0.169539	+	0.293649i	0.768719	+	0.639586i	$0.220894\pi$
$522$		0			0
$523$	−18.0070	−	31.1891i	−0.787391	−	1.36380i	−0.927560	−	0.373674i	$-0.878098\pi$
$523$	−18.0070	−	31.1891i	−0.787391	−	1.36380i	0.140169	−	0.990128i	$-0.455236\pi$
$524$	0.989757	+	0.830505i	0.0432378	+	0.0362808i
$525$		0			0
$526$	−0.806650	−	4.57474i	−0.0351716	−	0.199468i
$527$	5.25827	+	29.8212i	0.229054	+	1.29903i
$528$		0			0
$529$	14.9896	+	12.5777i	0.651720	+	0.546858i
$530$	2.85780	+	4.94986i	0.124135	+	0.215008i
$531$		0			0
$532$	−1.82705	+	3.16455i	−0.0792129	+	0.137201i
$533$	3.78209	−	1.37657i	0.163820	−	0.0596257i
$534$		0			0
$535$	3.65882	−	3.07011i	0.158184	−	0.132733i
$536$	−0.782338	−	0.284748i	−0.0337919	−	0.0122992i
$537$		0			0
$538$	0.352599	−	1.99969i	0.0152016	−	0.0862126i
$539$	−5.45676			−0.235039
$540$		0			0
$541$	−24.4147			−1.04967			−0.524834	−	0.851204i	$-0.675873\pi$
$541$	−24.4147			−1.04967			−0.524834	+	0.851204i	$0.675873\pi$
$542$	0.00434263	−	0.0246283i	0.000186532	−	0.00105787i
$543$		0			0
$544$	−8.83769	−	3.21666i	−0.378913	−	0.137913i
$545$	21.2013	−	17.7900i	0.908163	−	0.762039i
$546$		0			0
$547$	26.6514	−	9.70030i	1.13953	−	0.414755i	0.297786	−	0.954633i	$-0.403752\pi$
$547$	26.6514	−	9.70030i	1.13953	−	0.414755i	0.841743	+	0.539878i	$0.181530\pi$
$548$	8.45913	−	14.6516i	0.361356	−	0.625887i
$549$		0			0
$550$	1.93130	+	3.34512i	0.0823511	+	0.142636i
$551$	3.07040	+	2.57637i	0.130803	+	0.109757i
$552$		0			0
$553$	−6.20885	−	35.2121i	−0.264027	−	1.49737i
$554$	−0.0304702	−	0.172805i	−0.00129456	−	0.00734179i
$555$		0			0
$556$	−20.2925	−	17.0274i	−0.860593	−	0.722124i
$557$	18.4687	+	31.9887i	0.782542	+	1.35540i	0.930456	+	0.366403i	$0.119411\pi$
$557$	18.4687	+	31.9887i	0.782542	+	1.35540i	−0.147914	+	0.989000i	$0.547256\pi$
$558$		0			0
$559$	2.13113	−	3.69123i	0.0901372	−	0.156122i
$560$	40.6757	−	14.8047i	1.71886	−	0.625614i
$561$		0			0
$562$	−3.64785	+	3.06091i	−0.153875	+	0.129117i
$563$	−21.4019	−	7.78965i	−0.901982	−	0.328295i	−0.150935	−	0.988544i	$-0.548229\pi$
$563$	−21.4019	−	7.78965i	−0.901982	−	0.328295i	−0.751047	+	0.660249i	$0.770451\pi$
$564$		0			0
$565$	−6.06800	+	34.4133i	−0.255282	+	1.44778i
$566$	−4.63625			−0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	5.36030	−	30.3998i	0.224716	−	1.27443i	−0.638512	−	0.769611i	$-0.720450\pi$
$569$	5.36030	−	30.3998i	0.224716	−	1.27443i	0.863228	−	0.504814i	$-0.168439\pi$
$570$		0			0
$571$	−12.0473	−	4.38487i	−0.504165	−	0.183501i	0.0774015	−	0.997000i	$-0.475338\pi$
$571$	−12.0473	−	4.38487i	−0.504165	−	0.183501i	−0.581566	+	0.813499i	$0.697560\pi$
$572$	−2.87722	+	2.41427i	−0.120303	+	0.100946i
$573$		0			0
$574$	−2.59200	+	0.943409i	−0.108188	+	0.0393771i
$575$	−29.2354	+	50.6372i	−1.21920	+	2.11172i
$576$		0			0
$577$	11.7632	+	20.3745i	0.489708	+	0.848200i	0.999930	−	0.0118433i	$-0.00376992\pi$
$577$	11.7632	+	20.3745i	0.489708	+	0.848200i	−0.510222	+	0.860043i	$0.670437\pi$
$578$	0.579073	+	0.485900i	0.0240863	+	0.0202108i
$579$		0			0
$580$	−8.37388	−	47.4906i	−0.347706	−	1.97194i
$581$	4.74619	+	26.9170i	0.196905	+	1.11670i
$582$		0			0
$583$	−16.8793	−	14.1634i	−0.699068	−	0.586587i
$584$	1.47628	+	2.55699i	0.0610888	+	0.105809i
$585$		0			0
$586$	−1.61363	+	2.79489i	−0.0666584	+	0.115456i
$587$	−10.7007	+	3.89473i	−0.441665	+	0.160753i	−0.553274	−	0.832999i	$-0.686622\pi$
$587$	−10.7007	+	3.89473i	−0.441665	+	0.160753i	0.111609	+	0.993752i	$0.464400\pi$
$588$		0			0
$589$	−3.07018	+	2.57619i	−0.126505	+	0.106150i
$590$	−7.19824	−	2.61995i	−0.296347	−	0.107861i
$591$		0			0
$592$	3.29112	−	18.6649i	0.135264	−	0.767122i
$593$	−37.7324			−1.54948			−0.774742	−	0.632277i	$-0.782120\pi$
$593$	−37.7324			−1.54948			−0.774742	+	0.632277i	$0.782120\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	−3.29172	+	18.6682i	−0.134834	+	0.764681i
$597$		0			0
$598$	0.811429	+	0.295336i	0.0331818	+	0.0120772i
$599$	36.2785	−	30.4413i	1.48230	−	1.24380i	0.578611	−	0.815604i	$-0.303595\pi$
$599$	36.2785	−	30.4413i	1.48230	−	1.24380i	0.903687	−	0.428193i	$-0.140850\pi$
$600$		0			0
$601$	29.2314	−	10.6394i	1.19237	−	0.433989i	0.331818	−	0.943343i	$-0.392338\pi$
$601$	29.2314	−	10.6394i	1.19237	−	0.433989i	0.860557	+	0.509354i	$0.170116\pi$
$602$	−1.46054	+	2.52973i	−0.0595271	+	0.103104i
$603$		0			0
$604$	−7.02156	−	12.1617i	−0.285703	−	0.494853i
$605$	13.7149	+	11.5082i	0.557591	+	0.467874i
$606$		0			0
$607$	5.12027	+	29.0385i	0.207825	+	1.17864i	0.892932	+	0.450192i	$0.148645\pi$
$607$	5.12027	+	29.0385i	0.207825	+	1.17864i	−0.685106	+	0.728443i	$0.740244\pi$
$608$	−0.216153	−	1.22586i	−0.00876614	−	0.0497153i
$609$		0			0
$610$	−4.05356	−	3.40134i	−0.164124	−	0.137716i
$611$	0.423740	+	0.733939i	0.0171427	+	0.0296920i
$612$		0			0
$613$	3.05214	−	5.28646i	0.123275	−	0.213518i	−0.797782	−	0.602945i	$-0.793994\pi$
$613$	3.05214	−	5.28646i	0.123275	−	0.213518i	0.921057	+	0.389427i	$0.127327\pi$
$614$	−5.49225	+	1.99901i	−0.221649	+	0.0806737i
$615$		0			0
$616$	3.97366	−	3.33430i	0.160103	−	0.134343i
$617$	17.9670	+	6.53946i	0.723325	+	0.263269i	0.677337	−	0.735673i	$-0.263134\pi$
$617$	17.9670	+	6.53946i	0.723325	+	0.263269i	0.0459884	+	0.998942i	$0.485356\pi$
$618$		0			0
$619$	−1.17279	+	6.65125i	−0.0471386	+	0.267336i	−0.999263	−	0.0383731i	$-0.987782\pi$
$619$	−1.17279	+	6.65125i	−0.0471386	+	0.267336i	0.952125	+	0.305709i	$0.0988936\pi$
$620$	48.2198			1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	3.96856	−	22.5068i	0.158997	−	0.901716i
$624$		0			0
$625$	−9.87255	−	3.59331i	−0.394902	−	0.143733i
$626$	0.442625	−	0.371406i	0.0176908	−	0.0148444i
$627$		0			0
$628$	14.2284	−	5.17872i	0.567776	−	0.206654i
$629$	−11.4638	+	19.8559i	−0.457091	+	0.791705i
$630$		0			0
$631$	0.228453	+	0.395693i	0.00909458	+	0.0157523i	0.870537	−	0.492103i	$-0.163772\pi$
$631$	0.228453	+	0.395693i	0.00909458	+	0.0157523i	−0.861442	+	0.507855i	$0.830438\pi$
$632$	6.20472	+	5.20638i	0.246811	+	0.207099i
$633$		0			0
$634$	0.932131	+	5.28638i	0.0370196	+	0.209949i
$635$	−13.4940	−	76.5280i	−0.535491	−	3.03692i
$636$		0			0
$637$	−1.28361	−	1.07708i	−0.0508586	−	0.0426754i
$638$	−1.41173	−	2.44519i	−0.0558909	−	0.0968058i
$639$		0			0
$640$	−9.95805	+	17.2479i	−0.393627	+	0.681781i
$641$	−2.69789	+	0.981950i	−0.106560	+	0.0387847i	−0.394750	−	0.918789i	$-0.629169\pi$
$641$	−2.69789	+	0.981950i	−0.106560	+	0.0387847i	0.288190	+	0.957573i	$0.406947\pi$
$642$		0			0
$643$	−1.30445	+	1.09457i	−0.0514426	+	0.0431655i	−0.668146	−	0.744030i	$-0.732912\pi$
$643$	−1.30445	+	1.09457i	−0.0514426	+	0.0431655i	0.616704	+	0.787195i	$0.288468\pi$
$644$	36.6156	+	13.3270i	1.44286	+	0.525156i
$645$		0			0
$646$	−0.0849572	+	0.481816i	−0.00334260	+	0.0189568i
$647$	−36.1004			−1.41925			−0.709626	−	0.704579i	$-0.751136\pi$
$647$	−36.1004			−1.41925			−0.709626	+	0.704579i	$0.751136\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	−0.205966	+	1.16809i	−0.00807866	+	0.0458164i
$651$		0			0
$652$	1.93920	+	0.705812i	0.0759451	+	0.0276417i
$653$	33.3750	−	28.0050i	1.30606	−	1.09592i	0.317002	−	0.948425i	$-0.397324\pi$
$653$	33.3750	−	28.0050i	1.30606	−	1.09592i	0.989063	−	0.147494i	$-0.0471206\pi$
$654$		0			0
$655$	−2.30276	+	0.838137i	−0.0899764	+	0.0327487i
$656$	−10.0507	+	17.4083i	−0.392412	+	0.679678i
$657$		0			0
$658$	−0.290404	−	0.502994i	−0.0113211	−	0.0196087i
$659$	−19.5196	−	16.3789i	−0.760374	−	0.638030i	0.177850	−	0.984058i	$-0.443086\pi$
$659$	−19.5196	−	16.3789i	−0.760374	−	0.638030i	−0.938224	+	0.346028i	$0.887530\pi$
$660$		0			0
$661$	5.93307	+	33.6481i	0.230770	+	1.30876i	0.851342	+	0.524611i	$0.175789\pi$
$661$	5.93307	+	33.6481i	0.230770	+	1.30876i	−0.620572	+	0.784149i	$0.713100\pi$
$662$	0.0982712	+	0.557324i	0.00381942	+	0.0216610i
$663$		0			0
$664$	−4.74303	−	3.97988i	−0.184065	−	0.154449i
$665$	−3.46529	−	6.00207i	−0.134378	−	0.232750i
$666$		0			0
$667$	21.3702	−	37.0143i	0.827459	−	1.43320i
$668$	15.4656	−	5.62903i	0.598384	−	0.217794i
$669$		0			0
$670$	0.600255	−	0.503674i	0.0231899	−	0.0194586i
$671$	19.1693	+	6.97705i	0.740022	+	0.269346i
$672$		0			0
$673$	−5.13021	+	29.0949i	−0.197755	+	1.12153i	0.710685	+	0.703511i	$0.248385\pi$
$673$	−5.13021	+	29.0949i	−0.197755	+	1.12153i	−0.908440	+	0.418015i	$0.862726\pi$
$674$	1.10113			0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	−7.08141	+	40.1607i	−0.272161	+	1.54350i	0.475677	+	0.879620i	$0.342203\pi$
$677$	−7.08141	+	40.1607i	−0.272161	+	1.54350i	−0.747838	+	0.663881i	$0.768908\pi$
$678$		0			0
$679$	2.70155	+	0.983285i	0.103676	+	0.0377350i
$680$	9.08688	−	7.62479i	0.348466	−	0.292398i
$681$		0			0
$682$	2.65299	−	0.965610i	0.101588	−	0.0369751i
$683$	15.8213	−	27.4033i	0.605384	−	1.04856i	−0.386606	−	0.922245i	$-0.626353\pi$
$683$	15.8213	−	27.4033i	0.605384	−	1.04856i	0.991991	−	0.126312i	$-0.0403139\pi$
$684$		0			0
$685$	16.0441	+	27.7891i	0.613012	+	1.06177i
$686$	−1.93216	−	1.62128i	−0.0737704	−	0.0619007i
$687$		0			0
$688$	3.69649	+	20.9638i	0.140927	+	0.799238i
$689$	−1.17494	−	6.66340i	−0.0447616	−	0.253855i
$690$		0			0
$691$	−21.8972	−	18.3739i	−0.833008	−	0.698977i	0.122971	−	0.992410i	$-0.460758\pi$
$691$	−21.8972	−	18.3739i	−0.833008	−	0.698977i	−0.955980	+	0.293433i	$0.905202\pi$
$692$	21.5190	+	37.2719i	0.818028	+	1.41687i
$693$		0			0
$694$	−0.760438	+	1.31712i	−0.0288658	+	0.0499971i
$695$	47.2124	−	17.1839i	1.79087	−	0.651822i
$696$		0			0
$697$	18.6279	−	15.6306i	0.705581	−	0.592052i
$698$	−2.34067	−	0.851935i	−0.0885958	−	0.0322462i
$699$		0			0
$700$	−9.29418	+	52.7099i	−0.351287	+	1.99225i
$701$	7.52982			0.284397			0.142199	−	0.989838i	$-0.454583\pi$
$701$	7.52982			0.284397			0.142199	+	0.989838i	$0.454583\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	3.15459	−	17.8905i	0.118893	−	0.674275i
$705$		0			0
$706$	5.39655	+	1.96418i	0.203102	+	0.0739230i
$707$	−13.0236	+	10.9281i	−0.489803	+	0.410994i
$708$		0			0
$709$	−7.53069	+	2.74095i	−0.282821	+	0.102938i	−0.479536	−	0.877522i	$-0.659195\pi$
$709$	−7.53069	+	2.74095i	−0.282821	+	0.102938i	0.196715	+	0.980461i	$0.436973\pi$
$710$	−1.58981	+	2.75363i	−0.0596646	+	0.103342i
$711$		0			0
$712$	2.58857	+	4.48354i	0.0970108	+	0.168028i
$713$	32.7388	+	27.4711i	1.22608	+	1.02880i
$714$		0			0
$715$	−1.23702	−	7.01551i	−0.0462620	−	0.262365i
$716$	3.10924	+	17.6334i	0.116198	+	0.658990i
$717$		0			0
$718$	−0.655267	−	0.549835i	−0.0244544	−	0.0205196i
$719$	13.4913	+	23.3676i	0.503140	+	0.871464i	0.999993	+	0.00362928i	$0.00115524\pi$
$719$	13.4913	+	23.3676i	0.503140	+	0.871464i	−0.496854	+	0.867834i	$0.665511\pi$
$720$		0			0
$721$	14.2860	−	24.7440i	0.532037	−	0.921515i
$722$	3.02749	−	1.10192i	0.112672	−	0.0410091i
$723$		0			0
$724$	10.7615	−	9.03000i	0.399949	−	0.335597i
$725$	55.1679	+	20.0795i	2.04888	+	0.745733i
$726$		0			0
$727$	−2.55164	+	14.4711i	−0.0946353	+	0.536703i	0.900223	+	0.435429i	$0.143403\pi$
$727$	−2.55164	+	14.4711i	−0.0946353	+	0.536703i	−0.994859	+	0.101275i	$0.967708\pi$
$728$	1.59288			0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	4.47171	−	25.3603i	0.165392	−	0.937986i
$732$		0			0
$733$	29.4535	+	10.7202i	1.08789	+	0.395960i	0.822839	−	0.568275i	$-0.192389\pi$
$733$	29.4535	+	10.7202i	1.08789	+	0.395960i	0.265051	+	0.964234i	$0.414611\pi$
$734$	−0.330268	+	0.277128i	−0.0121904	+	0.0102290i
$735$		0			0
$736$	−12.4731	+	4.53984i	−0.459764	+	0.167341i
$737$	−1.51039	+	2.61607i	−0.0556359	+	0.0963642i
$738$		0			0
$739$	−0.241454	−	0.418211i	−0.00888205	−	0.0153842i	0.861550	−	0.507672i	$-0.169494\pi$
$739$	−0.241454	−	0.418211i	−0.00888205	−	0.0153842i	−0.870432	+	0.492288i	$0.836161\pi$
$740$	27.9682	+	23.4681i	1.02813	+	0.862704i
$741$		0			0
$742$	0.805225	+	4.56666i	0.0295608	+	0.167647i
$743$	−7.47568	−	42.3967i	−0.274256	−	1.55538i	−0.741315	−	0.671158i	$-0.765797\pi$
$743$	−7.47568	−	42.3967i	−0.274256	−	1.55538i	0.467058	−	0.884226i	$-0.345314\pi$
$744$		0			0
$745$	−27.5419	−	23.1104i	−1.00906	−	0.846701i
$746$	2.42578	+	4.20157i	0.0888140	+	0.153830i
$747$		0			0
$748$	−11.3462	+	19.6523i	−0.414860	+	0.718558i
$749$	3.64131	−	1.32533i	0.133051	−	0.0484264i
$750$		0			0
$751$	33.6459	−	28.2323i	1.22776	−	1.03021i	0.229375	−	0.973338i	$-0.426332\pi$
$751$	33.6459	−	28.2323i	1.22776	−	1.03021i	0.998381	−	0.0568722i	$-0.0181127\pi$
$752$	−3.97735	−	1.44764i	−0.145039	−	0.0527899i
$753$		0			0
$754$	0.150555	−	0.853843i	0.00548291	−	0.0310951i
$755$	26.6350			0.969346
$756$		0			0
$757$	22.4143			0.814661			0.407331	−	0.913281i	$-0.366460\pi$
$757$	22.4143			0.814661			0.407331	+	0.913281i	$0.366460\pi$
$758$	0.154387	−	0.875574i	0.00560760	−	0.0318023i
$759$		0			0
$760$	1.47531	+	0.536969i	0.0535152	+	0.0194779i
$761$	7.65795	−	6.42578i	0.277600	−	0.232934i	−0.493348	−	0.869832i	$-0.664227\pi$
$761$	7.65795	−	6.42578i	0.277600	−	0.232934i	0.770948	+	0.636898i	$0.219783\pi$
$762$		0			0
$763$	21.0998	−	7.67971i	0.763865	−	0.278024i
$764$	11.7768	−	20.3980i	0.426069	−	0.737972i
$765$		0			0
$766$	−0.00386367	−	0.00669207i	−0.000139600	−	0.000241794i
$767$	6.94667	+	5.82895i	0.250830	+	0.210471i
$768$		0			0
$769$	−1.30170	−	7.38231i	−0.0469405	−	0.266213i	0.952301	−	0.305161i	$-0.0987103\pi$
$769$	−1.30170	−	7.38231i	−0.0469405	−	0.266213i	−0.999241	+	0.0389483i	$0.987599\pi$
$770$	0.847775	+	4.80797i	0.0305517	+	0.173267i
$771$		0			0
$772$	13.3918	+	11.2371i	0.481982	+	0.404431i
$773$	−9.91954	−	17.1812i	−0.356781	−	0.617963i	0.630640	−	0.776076i	$-0.282793\pi$
$773$	−9.91954	−	17.1812i	−0.356781	−	0.617963i	−0.987421	+	0.158112i	$0.949459\pi$
$774$		0			0
$775$	−29.3521	+	50.8394i	−1.05436	+	1.82620i
$776$	−0.611986	+	0.222745i	−0.0219690	+	0.00799606i
$777$		0			0
$778$	−2.78030	+	2.33295i	−0.0996787	+	0.0836403i
$779$	3.02435	+	1.10077i	0.108359	+	0.0394393i
$780$		0			0
$781$	2.12855	−	12.0716i	0.0761654	−	0.431955i
$782$	5.21709			0.186563
$783$		0			0
$784$	8.36872			0.298883
$785$	−4.98689	+	28.2821i	−0.177990	+	1.00943i
$786$		0			0
$787$	−37.3323	−	13.5879i	−1.33075	−	0.484355i	−0.423866	−	0.905725i	$-0.639327\pi$
$787$	−37.3323	−	13.5879i	−1.33075	−	0.484355i	−0.906889	+	0.421370i	$0.861549\pi$
$788$	−11.1647	+	9.36828i	−0.397725	+	0.333731i
$789$		0			0
$790$	−7.16353	+	2.60731i	−0.254867	+	0.0927640i
$791$	−14.1752	+	24.5522i	−0.504013	+	0.872976i
$792$		0			0
$793$	3.13210	+	5.42495i	0.111224	+	0.192646i
$794$	−0.000325492	0	0.000273120i	−1.15513e−5	0	9.69268e-6i
$795$		0			0
$796$	3.55229	+	20.1460i	0.125908	+	0.714057i
$797$	1.58123	+	8.96761i	0.0560101	+	0.317649i	0.999921	−	0.0125505i	$-0.00399505\pi$
$797$	1.58123	+	8.96761i	0.0560101	+	0.317649i	−0.943911	+	0.330200i	$0.892884\pi$
$798$		0			0
$799$	3.92235	+	3.29124i	0.138763	+	0.116436i
$800$	−9.11632	−	15.7899i	−0.322311	−	0.558258i
$801$		0			0
$802$	2.18437	−	3.78344i	0.0771327	−	0.133598i
$803$	10.0669	−	3.66404i	0.355252	−	0.129301i
$804$		0			0
$805$	−56.6138	+	47.5046i	−1.99537	+	1.67432i
$806$	0.814669	+	0.296515i	0.0286955	+	0.0104443i
$807$		0			0
$808$	0.668767	−	3.79277i	0.0235272	−	0.133429i
$809$	−3.01910			−0.106146			−0.0530730	−	0.998591i	$-0.516902\pi$
$809$	−3.01910			−0.106146			−0.0530730	+	0.998591i	$0.516902\pi$
$810$		0			0
$811$	33.1722			1.16483			0.582416	−	0.812891i	$-0.302107\pi$
$811$	33.1722			1.16483			0.582416	+	0.812891i	$0.302107\pi$
$812$	6.79378	−	38.5295i	0.238415	−	1.35212i
$813$		0			0
$814$	2.00873	+	0.731117i	0.0704058	+	0.0256256i
$815$	−2.99833	+	2.51590i	−0.105027	+	0.0881282i
$816$		0			0
$817$	3.20277	−	1.16571i	0.112051	−	0.0407832i
$818$	2.01418	−	3.48866i	0.0704241	−	0.121978i
$819$		0			0
$820$	−19.3612	−	33.5345i	−0.676121	−	1.17108i
$821$	−32.7576	−	27.4869i	−1.14325	−	0.959298i	−0.143707	−	0.989620i	$-0.545902\pi$
$821$	−32.7576	−	27.4869i	−1.14325	−	0.959298i	−0.999540	+	0.0303224i	$0.990347\pi$
$822$		0			0
$823$	−6.11743	−	34.6936i	−0.213240	−	1.20934i	−0.883934	−	0.467611i	$-0.845115\pi$
$823$	−6.11743	−	34.6936i	−0.213240	−	1.20934i	0.670694	−	0.741734i	$-0.265996\pi$
$824$	1.12393	+	6.37410i	0.0391538	+	0.222052i
$825$		0			0
$826$	−4.76080	−	3.99478i	−0.165649	−	0.138996i
$827$	13.0190	+	22.5495i	0.452714	+	0.784125i	0.998554	−	0.0537655i	$-0.0171223\pi$
$827$	13.0190	+	22.5495i	0.452714	+	0.784125i	−0.545839	+	0.837890i	$0.683789\pi$
$828$		0			0
$829$	3.95134	−	6.84392i	0.137236	−	0.237699i	−0.789214	−	0.614119i	$-0.789512\pi$
$829$	3.95134	−	6.84392i	0.137236	−	0.237699i	0.926449	+	0.376420i	$0.122845\pi$
$830$	5.47597	−	1.99309i	0.190074	−	0.0691812i
$831$		0			0
$832$	4.27338	−	3.58579i	0.148153	−	0.124315i
$833$	−9.51326	−	3.46254i	−0.329615	−	0.119970i
$834$		0			0
$835$	−5.42052	+	30.7413i	−0.187585	+	1.06385i
$836$	−3.00344			−0.103876
$837$		0			0
$838$	−5.41213			−0.186959
$839$	−0.894009	+	5.07018i	−0.0308646	+	0.175042i	−0.996343	−	0.0854401i	$-0.972770\pi$
$839$	−0.894009	+	5.07018i	−0.0308646	+	0.175042i	0.965479	+	0.260482i	$0.0838815\pi$
$840$		0			0
$841$	−13.0751	−	4.75893i	−0.450864	−	0.164101i
$842$	4.04539	−	3.39449i	0.139413	−	0.116982i
$843$		0			0
$844$	38.6196	−	14.0564i	1.32934	−	0.483841i
$845$	−23.1939	+	40.1730i	−0.797894	+	1.38199i
$846$		0			0
$847$	7.26264	+	12.5793i	0.249547	+	0.432228i
$848$	25.8868	+	21.7216i	0.888955	+	0.745922i
$849$		0			0
$850$	1.24440	+	7.05733i	0.0426825	+	0.242065i
$851$	5.61906	+	31.8673i	0.192619	+	1.09240i
$852$		0			0
$853$	19.9098	+	16.7063i	0.681700	+	0.572014i	0.916503	−	0.400029i	$-0.131000\pi$
$853$	19.9098	+	16.7063i	0.681700	+	0.572014i	−0.234802	+	0.972043i	$0.575444\pi$
$854$	−2.14653	−	3.71791i	−0.0734529	−	0.127224i
$855$		0			0
$856$	−0.438904	+	0.760204i	−0.0150014	+	0.0259832i
$857$	−3.87072	+	1.40883i	−0.132221	+	0.0481246i	−0.407283	−	0.913302i	$-0.633524\pi$
$857$	−3.87072	+	1.40883i	−0.132221	+	0.0481246i	0.275062	+	0.961426i	$0.411302\pi$
$858$		0			0
$859$	−4.92523	+	4.13276i	−0.168047	+	0.141008i	−0.722933	−	0.690919i	$-0.757206\pi$
$859$	−4.92523	+	4.13276i	−0.168047	+	0.141008i	0.554886	+	0.831926i	$0.312762\pi$
$860$	−38.5338	−	14.0252i	−1.31399	−	0.478254i
$861$		0			0
$862$	−0.373199	+	2.11651i	−0.0127112	+	0.0720888i
$863$	−29.6195			−1.00826			−0.504129	−	0.863628i	$-0.668187\pi$
$863$	−29.6195			−1.00826			−0.504129	+	0.863628i	$0.668187\pi$
$864$		0			0
$865$	−81.6282			−2.77544
$866$	−0.0228476	+	0.129575i	−0.000776393	+	0.00440314i
$867$		0			0
$868$	36.7618	+	13.3802i	1.24778	+	0.454153i
$869$	22.5130	−	18.8906i	0.763700	−	0.640820i
$870$		0			0
$871$	−0.871665	+	0.317260i	−0.0295353	+	0.0107500i
$872$	−2.54326	+	4.40505i	−0.0861256	+	0.149174i
$873$		0			0
$874$	0.345251	+	0.597993i	0.0116783	+	0.0202274i
$875$	−34.3785	−	28.8470i	−1.16221	−	0.975206i
$876$		0			0
$877$	−5.53377	−	31.3835i	−0.186862	−	1.05975i	−0.923540	−	0.383503i	$-0.874718\pi$
$877$	−5.53377	−	31.3835i	−0.186862	−	1.05975i	0.736678	−	0.676244i	$-0.236393\pi$
$878$	0.904393	+	5.12907i	0.0305218	+	0.173098i
$879$		0			0
$880$	27.2546	+	22.8694i	0.918754	+	0.770926i
$881$	17.3932	+	30.1259i	0.585991	+	1.01497i	0.994751	+	0.102325i	$0.0326280\pi$
$881$	17.3932	+	30.1259i	0.585991	+	1.01497i	−0.408760	+	0.912642i	$0.634039\pi$
$882$		0			0
$883$	15.1882	−	26.3067i	0.511124	−	0.885292i	−0.488793	−	0.872400i	$-0.662563\pi$
$883$	15.1882	−	26.3067i	0.511124	−	0.885292i	0.999917	−	0.0128924i	$-0.00410388\pi$
$884$	−6.54807	+	2.38330i	−0.220235	+	0.0801591i
$885$		0			0
$886$	1.81026	−	1.51899i	0.0608168	−	0.0510314i
$887$	−47.0106	−	17.1105i	−1.57846	−	0.574513i	−0.603593	−	0.797293i	$-0.706265\pi$
$887$	−47.0106	−	17.1105i	−1.57846	−	0.574513i	−0.974869	+	0.222780i	$0.928487\pi$
$888$		0			0
$889$	10.9477	−	62.0877i	0.367175	−	2.08235i
$890$	−4.87263			−0.163331
$891$		0			0
$892$	−46.4515			−1.55531
$893$	−0.117679	+	0.667392i	−0.00393799	+	0.0223334i
$894$		0			0
$895$	−31.9123	−	11.6151i	−1.06671	−	0.388251i
$896$	−12.3778	+	10.3862i	−0.413513	+	0.346979i
$897$		0			0
$898$	3.57580	−	1.30148i	0.119326	−	0.0434311i
$899$	21.4556	−	37.1621i	0.715583	−	1.23943i
$900$		0			0
$901$	−20.4399	−	35.4029i	−0.680950	−	1.17944i
$902$	−1.73676	−	1.45732i	−0.0578278	−	0.0485233i
$903$		0			0
$904$	−1.11521	−	6.32469i	−0.0370914	−	0.210356i
$905$	4.62678	+	26.2398i	0.153799	+	0.872240i
$906$		0			0
$907$	−33.7552	−	28.3240i	−1.12082	−	0.940483i	−0.122178	−	0.992508i	$-0.538988\pi$
$907$	−33.7552	−	28.3240i	−1.12082	−	0.940483i	−0.998646	+	0.0520254i	$0.983432\pi$
$908$	−10.3273	−	17.8874i	−0.342723	−	0.593614i
$909$		0			0
$910$	−0.749593	+	1.29833i	−0.0248488	+	0.0430393i
$911$	−34.9361	+	12.7157i	−1.15749	+	0.421290i	−0.848199	−	0.529678i	$-0.822313\pi$
$911$	−34.9361	+	12.7157i	−1.15749	+	0.421290i	−0.309287	+	0.950969i	$0.600090\pi$
$912$		0			0
$913$	−17.2094	+	14.4404i	−0.569549	+	0.477908i
$914$	0.242000	+	0.0880809i	0.00800466	+	0.00291346i
$915$		0			0
$916$	4.74918	−	26.9340i	0.156917	−	0.889923i
$917$	−1.98815			−0.0656544
$918$		0			0
$919$	12.3976			0.408958			0.204479	−	0.978871i	$-0.434450\pi$
$919$	12.3976			0.408958			0.204479	+	0.978871i	$0.434450\pi$
$920$	2.90714	−	16.4872i	0.0958457	−	0.543568i
$921$		0			0
$922$	1.15623	+	0.420834i	0.0380785	+	0.0138594i
$923$	2.88345	−	2.41950i	0.0949098	−	0.0796388i
$924$		0			0
$925$	−41.7677	+	15.2022i	−1.37331	+	0.499845i
$926$	2.29545	−	3.97584i	0.0754333	−	0.130654i
$927$		0			0
$928$	6.66377	+	11.5420i	0.218749	+	0.378884i
$929$	−25.5768	−	21.4615i	−0.839149	−	0.704130i	0.118223	−	0.992987i	$-0.462280\pi$
$929$	−25.5768	−	21.4615i	−0.839149	−	0.704130i	−0.957372	+	0.288857i	$0.906725\pi$
$930$		0			0
$931$	−0.232676	−	1.31957i	−0.00762563	−	0.0432471i
$932$	−2.59984	−	14.7444i	−0.0851607	−	0.482970i
$933$		0			0
$934$	3.46532	+	2.90775i	0.113389	+	0.0951445i
$935$	−21.5199	−	37.2736i	−0.703777	−	1.21898i
$936$		0			0
$937$	12.4220	−	21.5156i	0.405810	−	0.702884i	−0.588605	−	0.808421i	$-0.700323\pi$
$937$	12.4220	−	21.5156i	0.405810	−	0.702884i	0.994415	+	0.105537i	$0.0336561\pi$
$938$	0.597383	−	0.217429i	0.0195052	−	0.00709932i
$939$		0			0
$940$	6.24596	−	5.24098i	0.203721	−	0.170942i
$941$	23.8963	+	8.69753i	0.778996	+	0.283531i	0.700754	−	0.713403i	$-0.252847\pi$
$941$	23.8963	+	8.69753i	0.778996	+	0.283531i	0.0782422	+	0.996934i	$0.475069\pi$
$942$		0			0
$943$	5.95957	−	33.7984i	0.194070	−	1.10063i
$944$	−45.2900			−1.47406
$945$		0			0
$946$	−2.40094			−0.0780612
$947$	−2.88780	+	16.3775i	−0.0938407	+	0.532197i	0.901256	+	0.433288i	$0.142647\pi$
$947$	−2.88780	+	16.3775i	−0.0938407	+	0.532197i	−0.995096	+	0.0989096i	$0.968465\pi$
$948$		0			0
$949$	3.09128	+	1.12514i	0.100347	+	0.0365234i
$950$	−0.726575	+	0.609669i	−0.0235732	+	0.0197803i
$951$		0			0
$952$	9.04339	−	3.29153i	0.293098	−	0.106679i
$953$	7.13357	−	12.3557i	0.231079	−	0.400240i	−0.727047	−	0.686588i	$-0.759108\pi$
$953$	7.13357	−	12.3557i	0.231079	−	0.400240i	0.958126	+	0.286347i	$0.0924411\pi$
$954$		0			0
$955$	22.3365	+	38.6879i	0.722791	+	1.25191i
$956$	−24.9898	−	20.9690i	−0.808229	−	0.678185i
$957$		0			0
$958$	−0.312581	−	1.77274i	−0.0100990	−	0.0572745i
$959$	4.52064	+	25.6378i	0.145979	+	0.827888i
$960$		0			0
$961$	9.12211	+	7.65436i	0.294262	+	0.246915i
$962$	0.328209	+	0.568474i	0.0105819	+	0.0183283i
$963$		0			0
$964$	−14.3013	+	24.7706i	−0.460613	+	0.797806i
$965$	−31.1573	+	11.3403i	−1.00299	+	0.365058i
$966$		0			0
$967$	−29.9407	+	25.1232i	−0.962827	+	0.807908i	−0.981411	−	0.191920i	$-0.938529\pi$
$967$	−29.9407	+	25.1232i	−0.962827	+	0.807908i	0.0185839	+	0.999827i	$0.494084\pi$
$968$	−3.09199	−	1.12539i	−0.0993802	−	0.0361714i
$969$		0			0
$970$	0.106439	−	0.603643i	0.00341753	−	0.0193818i
$971$	4.40370			0.141321			0.0706607	−	0.997500i	$-0.477489\pi$
$971$	4.40370			0.141321			0.0706607	+	0.997500i	$0.477489\pi$
$972$		0			0
$973$	40.7619			1.30677
$974$	−0.554674	+	3.14571i	−0.0177729	+	0.100795i
$975$		0			0
$976$	−29.3988	−	10.7003i	−0.941034	−	0.342508i
$977$	−32.2708	+	27.0784i	−1.03243	+	0.866316i	−0.991139	−	0.132831i	$-0.957593\pi$
$977$	−32.2708	+	27.0784i	−1.03243	+	0.866316i	−0.0412962	+	0.999147i	$0.513149\pi$
$978$		0			0
$979$	17.6517	−	6.42469i	0.564150	−	0.205334i
$980$	−8.06057	+	13.9613i	−0.257486	+	0.445978i
$981$		0			0
$982$	1.46804	+	2.54272i	0.0468470	+	0.0811413i
$983$	15.6473	+	13.1297i	0.499072	+	0.418771i	0.857264	−	0.514877i	$-0.172162\pi$
$983$	15.6473	+	13.1297i	0.499072	+	0.418771i	−0.358192	+	0.933648i	$0.616607\pi$
$984$		0			0
$985$	−4.80011	−	27.2228i	−0.152944	−	0.867390i
$986$	−0.909620	−	5.15871i	−0.0289682	−	0.164287i
$987$		0			0
$988$	−0.706510	−	0.592833i	−0.0224771	−	0.0188605i
$989$	−18.1723	−	31.4753i	−0.577844	−	1.00086i
$990$		0			0
$991$	−0.0340356	+	0.0589514i	−0.00108118	+	0.00187265i	−0.866565	−	0.499063i	$-0.833677\pi$
$991$	−0.0340356	+	0.0589514i	−0.00108118	+	0.00187265i	0.865484	+	0.500936i	$0.167011\pi$
$992$	−12.5229	+	4.55796i	−0.397602	+	0.144715i
$993$		0			0
$994$	−1.97613	+	1.65817i	−0.0626789	+	0.0525938i
$995$	−36.4596	−	13.2702i	−1.15585	−	0.420694i
$996$		0			0
$997$	1.84868	−	10.4844i	0.0585482	−	0.332043i	−0.941439	−	0.337184i	$-0.890525\pi$
$997$	1.84868	−	10.4844i	0.0585482	−	0.332043i	0.999987	+	0.00514123i	$0.00163651\pi$
$998$	4.26319			0.134949
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.s.649.2		12
3.2	odd	2		729.2.e.l.649.1		12
9.2	odd	6		729.2.e.k.163.2		12
9.4	even	3		729.2.e.j.406.2		12
9.5	odd	6		729.2.e.u.406.1		12
9.7	even	3		729.2.e.t.163.1		12
27.2	odd	18		729.2.c.a.487.4		12
27.4	even	9		729.2.e.j.325.2		12
27.5	odd	18		729.2.e.k.568.2		12
27.7	even	9		729.2.c.d.244.3		12
27.11	odd	18		729.2.a.e.1.3	yes	6
27.13	even	9	inner	729.2.e.s.82.2		12
27.14	odd	18		729.2.e.l.82.1		12
27.16	even	9		729.2.a.b.1.4	✓	6
27.20	odd	18		729.2.c.a.244.4		12
27.22	even	9		729.2.e.t.568.1		12
27.23	odd	18		729.2.e.u.325.1		12
27.25	even	9		729.2.c.d.487.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.4	✓	6	27.16	even	9
729.2.a.e.1.3	yes	6	27.11	odd	18
729.2.c.a.244.4		12	27.20	odd	18
729.2.c.a.487.4		12	27.2	odd	18
729.2.c.d.244.3		12	27.7	even	9
729.2.c.d.487.3		12	27.25	even	9
729.2.e.j.325.2		12	27.4	even	9
729.2.e.j.406.2		12	9.4	even	3
729.2.e.k.163.2		12	9.2	odd	6
729.2.e.k.568.2		12	27.5	odd	18
729.2.e.l.82.1		12	27.14	odd	18
729.2.e.l.649.1		12	3.2	odd	2
729.2.e.s.82.2		12	27.13	even	9	inner
729.2.e.s.649.2		12	1.1	even	1	trivial
729.2.e.t.163.1		12	9.7	even	3
729.2.e.t.568.1		12	27.22	even	9
729.2.e.u.325.1		12	27.23	odd	18
729.2.e.u.406.1		12	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0300370 - 0.170348i) q^{2} +(1.85127 + 0.673807i) q^{4} +(-2.86237 + 2.40182i) q^{5} +(-2.84868 + 1.03683i) q^{7} +(0.343364 - 0.594724i) q^{8} +O(q^{10})\)	\(q+(0.0300370 - 0.170348i) q^{2} +(1.85127 + 0.673807i) q^{4} +(-2.86237 + 2.40182i) q^{5} +(-2.84868 + 1.03683i) q^{7} +(0.343364 - 0.594724i) q^{8} +(0.323168 + 0.559743i) q^{10} +(-1.90875 - 1.60163i) q^{11} +(-0.132865 - 0.753515i) q^{13} +(0.0910570 + 0.516410i) q^{14} +(2.92734 + 2.45633i) q^{16} +(-2.31139 - 4.00345i) q^{17} +(0.305922 - 0.529872i) q^{19} +(-6.91738 + 2.51772i) q^{20} +(-0.330168 + 0.277044i) q^{22} +(-6.13091 - 2.23147i) q^{23} +(1.55622 - 8.82575i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(-1.13755 + 6.45137i) q^{29} +(-6.15539 - 2.24038i) q^{31} +(1.55849 - 1.30773i) q^{32} +(-0.751407 + 0.273490i) q^{34} +(5.66369 - 9.80980i) q^{35} +(-2.47984 - 4.29522i) q^{37} +(-0.0810738 - 0.0680290i) q^{38} +(0.445582 + 2.52702i) q^{40} +(0.913431 + 5.18032i) q^{41} +(4.26731 + 3.58070i) q^{43} +(-2.45442 - 4.25118i) q^{44} +(-0.564280 + 0.977362i) q^{46} +(-1.04082 + 0.378827i) q^{47} +(1.67762 - 1.40769i) q^{49} +(-1.45670 - 0.530197i) q^{50} +(0.261754 - 1.48448i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(-0.361503 + 2.05019i) q^{56} +(1.06481 + 0.387559i) q^{58} +(-9.07897 + 7.61816i) q^{59} +(-7.69327 + 2.80012i) q^{61} +(-0.566533 + 0.981264i) q^{62} +(3.64541 + 6.31404i) q^{64} +(2.19011 + 1.83772i) q^{65} +(-0.210520 - 1.19392i) q^{67} +(-1.58146 - 8.96889i) q^{68} +(-1.50096 - 1.25946i) q^{70} +(2.45973 + 4.26038i) q^{71} +(-2.14972 + 3.72343i) q^{73} +(-0.806169 + 0.293421i) q^{74} +(0.923375 - 0.774804i) q^{76} +(7.09803 + 2.58347i) q^{77} +(-2.04811 + 11.6154i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(1.56562 - 8.87910i) q^{83} +(16.2316 + 5.90782i) q^{85} +(0.738141 - 0.619374i) q^{86} +(-1.60792 + 0.585237i) q^{88} +(-3.76943 + 6.52884i) q^{89} +(1.15976 + 2.00876i) q^{91} +(-9.84638 - 8.26210i) q^{92} +(0.0332694 + 0.188680i) q^{94} +(0.396993 + 2.25146i) q^{95} +(-0.726481 - 0.609590i) q^{97} +(-0.189407 - 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

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