LMFDB - Embedded newform 729.2.e.u.325.1

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			325.1
Root			$-0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.u.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +O(q^{10})$	\(q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +(0.323168 - 0.559743i) q^{10} +(-2.34143 - 0.852210i) q^{11} +(-0.586130 - 0.491822i) q^{13} +(-0.401695 - 0.337062i) q^{14} +(-3.59091 - 1.30699i) q^{16} +(2.31139 - 4.00345i) q^{17} +(0.305922 + 0.529872i) q^{19} +(-1.27828 - 7.24949i) q^{20} +(0.405011 - 0.147412i) q^{22} +(-1.13295 + 6.42526i) q^{23} +(6.86521 - 5.76060i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(5.01827 - 4.21083i) q^{29} +(1.13747 - 6.45091i) q^{31} +(1.91177 - 0.695827i) q^{32} +(0.138854 + 0.787482i) q^{34} +(-5.66369 - 9.80980i) q^{35} +(-2.47984 + 4.29522i) q^{37} +(-0.0994517 - 0.0361975i) q^{38} +(1.96567 + 1.64939i) q^{40} +(-4.02958 - 3.38122i) q^{41} +(-5.23463 - 1.90525i) q^{43} +(2.45442 - 4.25118i) q^{44} +(-0.564280 - 0.977362i) q^{46} +(-0.192335 - 1.09079i) q^{47} +(-2.05791 + 0.749017i) q^{49} +(-0.269188 + 1.52664i) q^{50} +(1.15472 - 0.968928i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(1.59476 - 1.33816i) q^{56} +(-0.196769 + 1.11593i) q^{58} +(-11.1370 + 4.05354i) q^{59} +(1.42166 + 8.06263i) q^{61} +(0.566533 + 0.981264i) q^{62} +(3.64541 - 6.31404i) q^{64} +(2.68657 + 0.977832i) q^{65} +(-0.928705 - 0.779276i) q^{67} +(6.97656 + 5.85403i) q^{68} +(1.84120 + 0.670142i) q^{70} +(-2.45973 + 4.26038i) q^{71} +(-2.14972 - 3.72343i) q^{73} +(-0.148974 - 0.844873i) q^{74} +(-1.13269 + 0.412265i) q^{76} +(1.31166 - 7.43882i) q^{77} +(-9.03519 + 7.58143i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(-6.90671 + 5.79542i) q^{83} +(-2.99948 + 17.0109i) q^{85} +(0.905464 - 0.329562i) q^{86} +(0.297133 + 1.68512i) q^{88} +(3.76943 + 6.52884i) q^{89} +(1.15976 - 2.00876i) q^{91} +(-12.0784 - 4.39617i) q^{92} +(0.146767 + 0.123152i) q^{94} +(-1.75133 - 1.46954i) q^{95} +(0.891161 + 0.324356i) q^{97} +(0.189407 - 0.328062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.132507	+	0.111187i	−0.0936968	+	0.0786209i	−0.688433	−	0.725300i	$-0.741701\pi$
$2$	−0.132507	+	0.111187i	−0.0936968	+	0.0786209i	0.594736	+	0.803921i	$0.297257\pi$
$3$		0			0
$3$		0			0
$4$	−0.342101	+	1.94015i	−0.171050	+	0.970075i
$5$	−3.51122	+	1.27798i	−1.57027	+	0.571530i	−0.973059	−	0.230557i	$-0.925945\pi$
$5$	−3.51122	+	1.27798i	−1.57027	+	0.571530i	−0.597207	+	0.802087i	$0.703723\pi$
$6$		0			0
$7$	0.526414	+	2.98544i	0.198966	+	1.12839i	0.906657	+	0.421869i	$0.138626\pi$
$7$	0.526414	+	2.98544i	0.198966	+	1.12839i	−0.707691	+	0.706522i	$0.750263\pi$
$8$	−0.343364	−	0.594724i	−0.121398	−	0.210267i
$9$		0			0
$10$	0.323168	−	0.559743i	0.102195	−	0.177006i
$11$	−2.34143	−	0.852210i	−0.705967	−	0.256951i	−0.0360107	−	0.999351i	$-0.511465\pi$
$11$	−2.34143	−	0.852210i	−0.705967	−	0.256951i	−0.669957	+	0.742400i	$0.733687\pi$
$12$		0			0
$13$	−0.586130	−	0.491822i	−0.162563	−	0.136407i	0.557877	−	0.829923i	$-0.311616\pi$
$13$	−0.586130	−	0.491822i	−0.162563	−	0.136407i	−0.720441	+	0.693517i	$0.756060\pi$
$14$	−0.401695	−	0.337062i	−0.107358	−	0.0900837i
$15$		0			0
$16$	−3.59091	−	1.30699i	−0.897729	−	0.326746i
$17$	2.31139	−	4.00345i	0.560595	−	0.970979i	−0.436850	−	0.899534i	$-0.643906\pi$
$17$	2.31139	−	4.00345i	0.560595	−	0.970979i	0.997445	−	0.0714442i	$-0.0227608\pi$
$18$		0			0
$19$	0.305922	+	0.529872i	0.0701833	+	0.121561i	0.898982	−	0.437987i	$-0.144308\pi$
$19$	0.305922	+	0.529872i	0.0701833	+	0.121561i	−0.828798	+	0.559548i	$0.810975\pi$
$20$	−1.27828	−	7.24949i	−0.285832	−	1.62104i
$21$		0			0
$22$	0.405011	−	0.147412i	0.0863486	−	0.0314283i
$23$	−1.13295	+	6.42526i	−0.236236	+	1.33976i	0.603760	+	0.797166i	$0.293668\pi$
$23$	−1.13295	+	6.42526i	−0.236236	+	1.33976i	−0.839996	+	0.542593i	$0.817443\pi$
$24$		0			0
$25$	6.86521	−	5.76060i	1.37304	−	1.15212i
$26$	0.132351			0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	5.01827	−	4.21083i	0.931870	−	0.781932i	−0.0442820	−	0.999019i	$-0.514100\pi$
$29$	5.01827	−	4.21083i	0.931870	−	0.781932i	0.976152	+	0.217087i	$0.0696556\pi$
$30$		0			0
$31$	1.13747	−	6.45091i	0.204296	−	1.15862i	−0.694249	−	0.719735i	$-0.744263\pi$
$31$	1.13747	−	6.45091i	0.204296	−	1.15862i	0.898544	−	0.438883i	$-0.144626\pi$
$32$	1.91177	−	0.695827i	0.337956	−	0.123006i
$33$		0			0
$34$	0.138854	+	0.787482i	0.0238133	+	0.135052i
$35$	−5.66369	−	9.80980i	−0.957338	−	1.65816i
$36$		0			0
$37$	−2.47984	+	4.29522i	−0.407684	+	0.706129i	−0.994630	−	0.103497i	$-0.966997\pi$
$37$	−2.47984	+	4.29522i	−0.407684	+	0.706129i	0.586946	+	0.809626i	$0.300330\pi$
$38$	−0.0994517	−	0.0361975i	−0.0161332	−	0.00587200i
$39$		0			0
$40$	1.96567	+	1.64939i	0.310800	+	0.260792i
$41$	−4.02958	−	3.38122i	−0.629314	−	0.528057i	0.271402	−	0.962466i	$-0.412513\pi$
$41$	−4.02958	−	3.38122i	−0.629314	−	0.528057i	−0.900716	+	0.434409i	$0.856957\pi$
$42$		0			0
$43$	−5.23463	−	1.90525i	−0.798273	−	0.290548i	−0.0895024	−	0.995987i	$-0.528528\pi$
$43$	−5.23463	−	1.90525i	−0.798273	−	0.290548i	−0.708771	+	0.705439i	$0.750750\pi$
$44$	2.45442	−	4.25118i	0.370018	−	0.640889i
$45$		0			0
$46$	−0.564280	−	0.977362i	−0.0831986	−	0.144104i
$47$	−0.192335	−	1.09079i	−0.0280550	−	0.159108i	0.967562	−	0.252635i	$-0.0812971\pi$
$47$	−0.192335	−	1.09079i	−0.0280550	−	0.159108i	−0.995617	+	0.0935267i	$0.970186\pi$
$48$		0			0
$49$	−2.05791	+	0.749017i	−0.293987	+	0.107002i
$50$	−0.269188	+	1.52664i	−0.0380690	+	0.215900i
$51$		0			0
$52$	1.15472	−	0.968928i	0.160131	−	0.134366i
$53$	−8.84310			−1.21469			−0.607346	−	0.794437i	$-0.707766\pi$
$53$	−8.84310			−1.21469			−0.607346	+	0.794437i	$0.707766\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	1.59476	−	1.33816i	0.213109	−	0.178820i
$57$		0			0
$58$	−0.196769	+	1.11593i	−0.0258370	+	0.146529i
$59$	−11.1370	+	4.05354i	−1.44992	+	0.527726i	−0.942568	−	0.334016i	$-0.891596\pi$
$59$	−11.1370	+	4.05354i	−1.44992	+	0.527726i	−0.507347	+	0.861742i	$0.669374\pi$
$60$		0			0
$61$	1.42166	+	8.06263i	0.182025	+	1.03231i	0.929719	+	0.368270i	$0.120050\pi$
$61$	1.42166	+	8.06263i	0.182025	+	1.03231i	−0.747694	+	0.664043i	$0.768839\pi$
$62$	0.566533	+	0.981264i	0.0719498	+	0.124621i
$63$		0			0
$64$	3.64541	−	6.31404i	0.455677	−	0.789255i
$65$	2.68657	+	0.977832i	0.333228	+	0.121285i
$66$		0			0
$67$	−0.928705	−	0.779276i	−0.113459	−	0.0952037i	0.584293	−	0.811543i	$-0.301372\pi$
$67$	−0.928705	−	0.779276i	−0.113459	−	0.0952037i	−0.697752	+	0.716339i	$0.745816\pi$
$68$	6.97656	+	5.85403i	0.846032	+	0.709905i
$69$		0			0
$70$	1.84120	+	0.670142i	0.220066	+	0.0800973i
$71$	−2.45973	+	4.26038i	−0.291916	+	0.505614i	−0.974263	−	0.225415i	$-0.927626\pi$
$71$	−2.45973	+	4.26038i	−0.291916	+	0.505614i	0.682346	+	0.731029i	$0.260960\pi$
$72$		0			0
$73$	−2.14972	−	3.72343i	−0.251606	−	0.435795i	0.712362	−	0.701812i	$-0.247625\pi$
$73$	−2.14972	−	3.72343i	−0.251606	−	0.435795i	−0.963968	+	0.266017i	$0.914292\pi$
$74$	−0.148974	−	0.844873i	−0.0173179	−	0.0982145i
$75$		0			0
$76$	−1.13269	+	0.412265i	−0.129928	+	0.0472900i
$77$	1.31166	−	7.43882i	0.149478	−	0.847732i
$78$		0			0
$79$	−9.03519	+	7.58143i	−1.01654	+	0.852977i	−0.989189	−	0.146649i	$-0.953151\pi$
$79$	−9.03519	+	7.58143i	−1.01654	+	0.852977i	−0.0273498	+	0.999626i	$0.508707\pi$
$80$	14.2788			1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	−6.90671	+	5.79542i	−0.758110	+	0.636130i	−0.937634	−	0.347624i	$-0.886989\pi$
$83$	−6.90671	+	5.79542i	−0.758110	+	0.636130i	0.179524	+	0.983754i	$0.442544\pi$
$84$		0			0
$85$	−2.99948	+	17.0109i	−0.325339	+	1.84509i
$86$	0.905464	−	0.329562i	0.0976387	−	0.0355376i
$87$		0			0
$88$	0.297133	+	1.68512i	0.0316744	+	0.179635i
$89$	3.76943	+	6.52884i	0.399558	+	0.692055i	0.993671	−	0.112326i	$-0.0358302\pi$
$89$	3.76943	+	6.52884i	0.399558	+	0.692055i	−0.594113	+	0.804382i	$0.702497\pi$
$90$		0			0
$91$	1.15976	−	2.00876i	0.121576	−	0.210575i
$92$	−12.0784	−	4.39617i	−1.25926	−	0.458332i
$93$		0			0
$94$	0.146767	+	0.123152i	0.0151379	+	0.0127022i
$95$	−1.75133	−	1.46954i	−0.179682	−	0.150771i
$96$		0			0
$97$	0.891161	+	0.324356i	0.0904837	+	0.0329334i	0.386865	−	0.922136i	$-0.373558\pi$
$97$	0.891161	+	0.324356i	0.0904837	+	0.0329334i	−0.296382	+	0.955070i	$0.595780\pi$
$98$	0.189407	−	0.328062i	0.0191330	−	0.0331393i
$99$		0			0
$100$	8.82783	+	15.2902i	0.882783	+	1.52902i
$101$	0.973846	+	5.52295i	0.0969013	+	0.549554i	0.994148	+	0.108025i	$0.0344527\pi$
$101$	0.973846	+	5.52295i	0.0969013	+	0.549554i	−0.897247	+	0.441529i	$0.854436\pi$
$102$		0			0
$103$	8.85662	−	3.22355i	0.872669	−	0.317625i	0.133421	−	0.991059i	$-0.457404\pi$
$103$	8.85662	−	3.22355i	0.872669	−	0.317625i	0.739247	+	0.673434i	$0.235181\pi$
$104$	−0.0912421	+	0.517460i	−0.00894702	+	0.0507411i
$105$		0			0
$106$	1.17177	−	0.983235i	0.113813	−	0.0955003i
$107$	1.27825			0.123573			0.0617864	−	0.998089i	$-0.480320\pi$
$107$	1.27825			0.123573			0.0617864	+	0.998089i	$0.480320\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	−1.23369	+	1.03519i	−0.117628	+	0.0987016i
$111$		0			0
$112$	2.01162	−	11.4085i	0.190081	−	1.07800i
$113$	8.78797	−	3.19856i	0.826703	−	0.300895i	0.106198	−	0.994345i	$-0.466132\pi$
$113$	8.78797	−	3.19856i	0.826703	−	0.300895i	0.720505	+	0.693450i	$0.243910\pi$
$114$		0			0
$115$	−4.23332	−	24.0084i	−0.394759	−	2.23879i
$116$	6.45289	+	11.1767i	0.599136	+	1.03773i
$117$		0			0
$118$	1.02503	−	1.77541i	0.0943621	−	0.163440i
$119$	13.1688	+	4.79306i	1.20718	+	0.439379i
$120$		0			0
$121$	−3.67046	−	3.07989i	−0.333679	−	0.279990i
$122$	−1.08484	−	0.910287i	−0.0982166	−	0.0824135i
$123$		0			0
$124$	12.1266	+	4.41372i	1.08900	+	0.396364i
$125$	−7.40194	+	12.8205i	−0.662050	+	1.14670i
$126$		0			0
$127$	−10.3984	−	18.0106i	−0.922710	−	1.59818i	−0.795204	−	0.606342i	$-0.792636\pi$
$127$	−10.3984	−	18.0106i	−0.922710	−	1.59818i	−0.127505	−	0.991838i	$-0.540697\pi$
$128$	0.925555	+	5.24909i	0.0818083	+	0.463958i
$129$		0			0
$130$	−0.464712	+	0.169141i	−0.0407579	+	0.0148347i
$131$	0.113884	−	0.645866i	0.00995006	−	0.0564296i	−0.979428	−	0.201792i	$-0.935324\pi$
$131$	0.113884	−	0.645866i	0.00995006	−	0.0564296i	0.989379	+	0.145362i	$0.0464347\pi$
$132$		0			0
$133$	−1.42086	+	1.19224i	−0.123204	+	0.103381i
$134$	0.209705			0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	−6.57849	+	5.52001i	−0.562038	+	0.471606i	−0.878993	−	0.476835i	$-0.841784\pi$
$137$	−6.57849	+	5.52001i	−0.562038	+	0.471606i	0.316955	+	0.948441i	$0.397340\pi$
$138$		0			0
$139$	2.33490	−	13.2419i	0.198043	−	1.12316i	−0.709974	−	0.704228i	$-0.751293\pi$
$139$	2.33490	−	13.2419i	0.198043	−	1.12316i	0.908017	−	0.418932i	$-0.137596\pi$
$140$	20.9700	−	7.63247i	1.77229	−	0.645061i
$141$		0			0
$142$	−0.147766	−	0.838021i	−0.0124002	−	0.0703251i
$143$	0.953247	+	1.65107i	0.0797145	+	0.138070i
$144$		0			0
$145$	−12.2389	+	21.1984i	−1.01639	+	1.76043i
$146$	0.698851	+	0.254361i	0.0578373	+	0.0210511i
$147$		0			0
$148$	−7.48500	−	6.28066i	−0.615264	−	0.516267i
$149$	−7.37093	−	6.18495i	−0.603850	−	0.506691i	0.288830	−	0.957380i	$-0.406734\pi$
$149$	−7.37093	−	6.18495i	−0.603850	−	0.506691i	−0.892681	+	0.450690i	$0.851178\pi$
$150$		0			0
$151$	6.69832	+	2.43799i	0.545101	+	0.198401i	0.599869	−	0.800098i	$-0.295219\pi$
$151$	6.69832	+	2.43799i	0.545101	+	0.198401i	−0.0547672	+	0.998499i	$0.517442\pi$
$152$	0.210085	−	0.363878i	0.0170402	−	0.0295144i
$153$		0			0
$154$	0.653293	+	1.13154i	0.0526439	+	0.0911818i
$155$	4.25023	+	24.1042i	0.341386	+	1.93610i
$156$		0			0
$157$	−7.22226	+	2.62869i	−0.576399	+	0.209792i	−0.613737	−	0.789511i	$-0.710334\pi$
$157$	−7.22226	+	2.62869i	−0.576399	+	0.209792i	0.0373379	+	0.999303i	$0.488112\pi$
$158$	0.354274	−	2.00919i	0.0281845	−	0.159842i
$159$		0			0
$160$	−5.82339	+	4.88640i	−0.460379	+	0.386304i
$161$	−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	$0.486938\pi$
$164$	7.93859	−	6.66126i	0.619899	−	0.520157i
$165$		0			0
$166$	0.270815	−	1.53587i	0.0210193	−	0.119207i
$167$	7.85026	−	2.85726i	0.607472	−	0.221102i	−0.0199249	−	0.999801i	$-0.506343\pi$
$167$	7.85026	−	2.85726i	0.607472	−	0.221102i	0.627397	+	0.778700i	$0.284120\pi$
$168$		0			0
$169$	−2.15577	−	12.2260i	−0.165828	−	0.940458i
$170$	−1.49393	−	2.58757i	−0.114580	−	0.198458i
$171$		0			0
$172$	5.48724	−	9.50417i	0.418398	−	0.724686i
$173$	20.5283	+	7.47170i	1.56074	+	0.568063i	0.970906	−	0.239462i	$-0.0769710\pi$
$173$	20.5283	+	7.47170i	1.56074	+	0.568063i	0.589834	+	0.807525i	$0.299193\pi$
$174$		0			0
$175$	20.8119	+	17.4632i	1.57323	+	1.32010i
$176$	7.29404	+	6.12043i	0.549809	+	0.461345i
$177$		0			0
$178$	−1.22540	−	0.446008i	−0.0918474	−	0.0334297i
$179$	−4.54433	+	7.87101i	−0.339659	+	0.588307i	−0.984369	−	0.176121i	$-0.943645\pi$
$179$	−4.54433	+	7.87101i	−0.339659	+	0.588307i	0.644709	+	0.764428i	$0.276978\pi$
$180$		0			0
$181$	3.56539	+	6.17543i	0.265013	+	0.459016i	0.967567	−	0.252614i	$-0.0812904\pi$
$181$	3.56539	+	6.17543i	0.265013	+	0.459016i	−0.702554	+	0.711630i	$0.747957\pi$
$182$	0.0696712	+	0.395125i	0.00516437	+	0.0292886i
$183$		0			0
$184$	4.21027	−	1.53241i	0.310385	−	0.112971i
$185$	3.21808	−	18.2506i	0.236598	−	1.34181i
$186$		0			0
$187$	−8.82374	+	7.40399i	−0.645256	+	0.541434i
$188$	2.18209			0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	−9.15854	+	7.68493i	−0.662689	+	0.556062i	−0.910891	−	0.412646i	$-0.864605\pi$
$191$	−9.15854	+	7.68493i	−0.662689	+	0.556062i	0.248203	+	0.968708i	$0.420160\pi$
$192$		0			0
$193$	−1.54089	+	8.73883i	−0.110916	+	0.629034i	0.877776	+	0.479071i	$0.159027\pi$
$193$	−1.54089	+	8.73883i	−0.110916	+	0.629034i	−0.988692	+	0.149963i	$0.952085\pi$
$194$	−0.154149	+	0.0561058i	−0.0110673	+	0.00402816i
$195$		0			0
$196$	−0.749193	−	4.24889i	−0.0535138	−	0.303492i
$197$	3.69895	+	6.40677i	0.263539	+	0.456464i	0.967180	−	0.254093i	$-0.0817768\pi$
$197$	3.69895	+	6.40677i	0.263539	+	0.456464i	−0.703641	+	0.710556i	$0.748443\pi$
$198$		0			0
$199$	5.19187	−	8.99259i	0.368042	−	0.637468i	−0.621217	−	0.783638i	$-0.713362\pi$
$199$	5.19187	−	8.99259i	0.368042	−	0.637468i	0.989259	+	0.146171i	$0.0466948\pi$
$200$	−5.78323	−	2.10493i	−0.408936	−	0.148841i
$201$		0			0
$202$	−0.743121	−	0.623553i	−0.0522858	−	0.0438730i
$203$	15.2129	+	12.7651i	1.06774	+	0.895936i
$204$		0			0
$205$	18.4699	+	6.72248i	1.28999	+	0.469518i
$206$	−0.815151	+	1.41188i	−0.0567942	+	0.0983705i
$207$		0			0
$208$	1.46194	+	2.53215i	0.101367	+	0.175573i
$209$	−0.264732	−	1.50137i	−0.0183119	−	0.103852i
$210$		0			0
$211$	−19.6031	+	7.13493i	−1.34953	+	0.491189i	−0.912801	−	0.408404i	$-0.866085\pi$
$211$	−19.6031	+	7.13493i	−1.34953	+	0.491189i	−0.436729	+	0.899593i	$0.643863\pi$
$212$	3.02523	−	17.1569i	0.207774	−	1.17834i
$213$		0			0
$214$	−0.169377	+	0.142124i	−0.0115784	+	0.00971540i
$215$	20.8148			1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	0.981466	−	0.823548i	0.0664733	−	0.0557777i
$219$		0			0
$220$	−3.18509	+	18.0635i	−0.214739	+	1.21784i
$221$	−3.32376	+	1.20975i	−0.223580	+	0.0813765i
$222$		0			0
$223$	4.09436	+	23.2203i	0.274179	+	1.55494i	0.741558	+	0.670888i	$0.234087\pi$
$223$	4.09436	+	23.2203i	0.274179	+	1.55494i	−0.467380	+	0.884057i	$0.654802\pi$
$224$	3.08373	+	5.34118i	0.206041	+	0.356873i
$225$		0			0
$226$	−0.808832	+	1.40094i	−0.0538027	+	0.0931890i
$227$	−9.85186	−	3.58578i	−0.653891	−	0.237997i	−0.00629435	−	0.999980i	$-0.502004\pi$
$227$	−9.85186	−	3.58578i	−0.653891	−	0.237997i	−0.647597	+	0.761983i	$0.724226\pi$
$228$		0			0
$229$	−10.6345	−	8.92345i	−0.702751	−	0.589678i	0.219804	−	0.975544i	$-0.429458\pi$
$229$	−10.6345	−	8.92345i	−0.702751	−	0.589678i	−0.922555	+	0.385866i	$0.873903\pi$
$230$	3.23036	+	2.71059i	0.213004	+	0.178731i
$231$		0			0
$232$	−4.22738	−	1.53864i	−0.277541	−	0.101017i
$233$	3.79982	−	6.58149i	0.248935	−	0.431167i	−0.714296	−	0.699844i	$-0.753253\pi$
$233$	3.79982	−	6.58149i	0.248935	−	0.431167i	0.963230	+	0.268676i	$0.0865862\pi$
$234$		0			0
$235$	2.06934	+	3.58420i	0.134989	+	0.233807i
$236$	−4.05449	−	22.9942i	−0.263925	−	1.49679i
$237$		0			0
$238$	−2.27789	+	0.829083i	−0.147654	+	0.0537415i
$239$	−2.87539	+	16.3071i	−0.185993	+	1.05482i	0.738679	+	0.674057i	$0.235450\pi$
$239$	−2.87539	+	16.3071i	−0.185993	+	1.05482i	−0.924673	+	0.380763i	$0.875661\pi$
$240$		0			0
$241$	−11.1218	+	9.33230i	−0.716419	+	0.601147i	−0.926392	−	0.376560i	$-0.877107\pi$
$241$	−11.1218	+	9.33230i	−0.716419	+	0.601147i	0.209973	+	0.977707i	$0.432662\pi$
$242$	0.828806			0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	6.26854	−	5.25993i	0.400482	−	0.336044i
$246$		0			0
$247$	0.0812926	−	0.461033i	0.00517252	−	0.0293348i
$248$	−4.22708	+	1.53853i	−0.268420	+	0.0976968i
$249$		0			0
$250$	−0.444664	−	2.52181i	−0.0281230	−	0.159493i
$251$	4.52591	+	7.83910i	0.285673	+	0.494800i	0.972772	−	0.231764i	$-0.0744497\pi$
$251$	4.52591	+	7.83910i	0.285673	+	0.494800i	−0.687099	+	0.726563i	$0.741116\pi$
$252$		0			0
$253$	8.12838	−	14.0788i	0.511027	−	0.885125i
$254$	3.38040	+	1.23037i	0.212105	+	0.0772000i
$255$		0			0
$256$	10.4639	+	8.78028i	0.653995	+	0.548767i
$257$	−7.43054	−	6.23496i	−0.463504	−	0.388926i	0.380914	−	0.924610i	$-0.375609\pi$
$257$	−7.43054	−	6.23496i	−0.463504	−	0.388926i	−0.844418	+	0.535684i	$0.820054\pi$
$258$		0			0
$259$	−14.1285	−	5.14237i	−0.877905	−	0.319531i
$260$	−2.81622	+	4.87783i	−0.174654	+	0.302510i
$261$		0			0
$262$	0.0567214	+	0.0982443i	0.00350426	+	0.00606955i
$263$	4.66336	+	26.4473i	0.287555	+	1.63081i	0.696012	+	0.718030i	$0.254956\pi$
$263$	4.66336	+	26.4473i	0.287555	+	1.63081i	−0.408457	+	0.912778i	$0.633933\pi$
$264$		0			0
$265$	31.0501	−	11.3013i	1.90739	−	0.694233i
$266$	0.0557126	−	0.315962i	0.00341596	−	0.0193729i
$267$		0			0
$268$	1.82962	−	1.53524i	0.111762	−	0.0937794i
$269$	−11.7388			−0.715729			−0.357865	−	0.933774i	$-0.616495\pi$
$269$	−11.7388			−0.715729			−0.357865	+	0.933774i	$0.616495\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	−13.5325	+	11.3551i	−0.820526	+	0.688503i
$273$		0			0
$274$	0.257945	−	1.46288i	0.0155831	−	0.0883759i
$275$	−20.9836	+	7.63742i	−1.26536	+	0.460554i
$276$		0			0
$277$	−0.176153	−	0.999013i	−0.0105840	−	0.0600249i	0.979058	−	0.203580i	$-0.0652577\pi$
$277$	−0.176153	−	0.999013i	−0.0105840	−	0.0600249i	−0.989642	+	0.143555i	$0.954147\pi$
$278$	1.16293	+	2.01425i	0.0697479	+	0.120807i
$279$		0			0
$280$	−3.88942	+	6.73667i	−0.232437	+	0.402593i
$281$	−25.8692	−	9.41563i	−1.54323	−	0.561689i	−0.576412	−	0.817159i	$-0.695548\pi$
$281$	−25.8692	−	9.41563i	−1.54323	−	0.561689i	−0.966817	+	0.255470i	$0.917770\pi$
$282$		0			0
$283$	−20.5322	−	17.2286i	−1.22051	−	1.02413i	−0.998798	−	0.0490201i	$-0.984390\pi$
$283$	−20.5322	−	17.2286i	−1.22051	−	1.02413i	−0.221715	−	0.975112i	$-0.571165\pi$
$284$	−7.42430	−	6.22973i	−0.440551	−	0.369666i
$285$		0			0
$286$	−0.309889	−	0.112791i	−0.0183241	−	0.00666944i
$287$	7.97320	−	13.8100i	0.470643	−	0.815178i
$288$		0			0
$289$	−2.18506	−	3.78464i	−0.128533	−	0.222626i
$290$	−0.735239	−	4.16975i	−0.0431747	−	0.244856i
$291$		0			0
$292$	7.95944	−	2.89700i	0.465791	−	0.169534i
$293$	−3.23980	+	18.3738i	−0.189271	+	1.07341i	0.731073	+	0.682299i	$0.239020\pi$
$293$	−3.23980	+	18.3738i	−0.189271	+	1.07341i	−0.920344	+	0.391110i	$0.872091\pi$
$294$		0			0
$295$	33.9241	−	28.4657i	1.97514	−	1.65734i
$296$	3.40596			0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	3.82413	−	3.20883i	0.221155	−	0.185571i
$300$		0			0
$301$	2.93243	−	16.6306i	0.169022	−	0.958573i
$302$	−1.15865	+	0.421713i	−0.0666727	+	0.0242669i
$303$		0			0
$304$	−0.406004	−	2.30256i	−0.0232859	−	0.132061i
$305$	−15.2956	−	26.4928i	−0.875825	−	1.51697i
$306$		0			0
$307$	−16.8946	+	29.2624i	−0.964227	+	1.67009i	−0.252551	+	0.967584i	$0.581269\pi$
$307$	−16.8946	+	29.2624i	−0.964227	+	1.67009i	−0.711677	+	0.702507i	$0.752064\pi$
$308$	13.9837	+	5.08965i	0.796795	+	0.290010i
$309$		0			0
$310$	−3.24326	−	2.72142i	−0.184205	−	0.154566i
$311$	−26.5715	−	22.2961i	−1.50673	−	1.26430i	−0.869833	−	0.493346i	$-0.835774\pi$
$311$	−26.5715	−	22.2961i	−1.50673	−	1.26430i	−0.636896	−	0.770950i	$-0.719782\pi$
$312$		0			0
$313$	−3.13893	−	1.14248i	−0.177423	−	0.0645766i	0.251781	−	0.967784i	$-0.418984\pi$
$313$	−3.13893	−	1.14248i	−0.177423	−	0.0645766i	−0.429204	+	0.903208i	$0.641206\pi$
$314$	0.664726	−	1.15134i	0.0375127	−	0.0649739i
$315$		0			0
$316$	−11.6182	−	20.1232i	−0.653572	−	1.13202i
$317$	−5.38879	−	30.5613i	−0.302665	−	1.71650i	−0.634299	−	0.773088i	$-0.718711\pi$
$317$	−5.38879	−	30.5613i	−0.302665	−	1.71650i	0.331634	−	0.943408i	$-0.392400\pi$
$318$		0			0
$319$	−15.3384	+	5.58274i	−0.858788	+	0.312573i
$320$	−4.73063	+	26.8288i	−0.264451	+	1.49977i
$321$		0			0
$322$	2.62081	−	2.19912i	0.146052	−	0.122552i
$323$	2.82842			0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	−0.138801	+	0.116468i	−0.00768749	+	0.00645057i
$327$		0			0
$328$	−0.627279	+	3.55747i	−0.0346357	+	0.196429i
$329$	3.15524	−	1.14841i	0.173954	−	0.0633141i
$330$		0			0
$331$	0.568121	+	3.22197i	0.0312267	+	0.177096i	0.996432	−	0.0843970i	$-0.0268964\pi$
$331$	0.568121	+	3.22197i	0.0312267	+	0.177096i	−0.965205	+	0.261493i	$0.915785\pi$
$332$	−8.88119	−	15.3827i	−0.487419	−	0.844234i
$333$		0			0
$334$	−0.722527	+	1.25145i	−0.0395349	+	0.0684765i
$335$	4.25679	+	1.54934i	0.232573	+	0.0846497i
$336$		0			0
$337$	4.87649	+	4.09186i	0.265639	+	0.222898i	0.765872	−	0.642993i	$-0.222308\pi$
$337$	4.87649	+	4.09186i	0.265639	+	0.222898i	−0.500232	+	0.865891i	$0.666752\pi$
$338$	1.64502	+	1.38034i	0.0894773	+	0.0750803i
$339$		0			0
$340$	−31.9776	−	11.6389i	−1.73423	−	0.631207i
$341$	−8.16083	+	14.1350i	−0.441934	+	0.765452i
$342$		0			0
$343$	7.29078	+	12.6280i	0.393665	+	0.681848i
$344$	0.664286	+	3.76735i	0.0358159	+	0.203122i
$345$		0			0
$346$	−3.55091	+	1.29242i	−0.190898	+	0.0694812i
$347$	−1.52679	+	8.65883i	−0.0819622	+	0.464831i	0.916009	+	0.401158i	$0.131392\pi$
$347$	−1.52679	+	8.65883i	−0.0819622	+	0.464831i	−0.997971	+	0.0636721i	$0.979719\pi$
$348$		0			0
$349$	11.0312	−	9.25628i	0.590487	−	0.495478i	−0.297885	−	0.954602i	$-0.596281\pi$
$349$	11.0312	−	9.25628i	0.590487	−	0.495478i	0.888372	+	0.459124i	$0.151837\pi$
$350$	−4.69941			−0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	25.4330	−	21.3409i	1.35366	−	1.13586i	0.375781	−	0.926709i	$-0.377375\pi$
$353$	25.4330	−	21.3409i	1.35366	−	1.13586i	0.977883	−	0.209150i	$-0.0670699\pi$
$354$		0			0
$355$	3.19198	−	18.1026i	0.169413	−	0.960787i
$356$	−13.9564	+	5.07973i	−0.739690	+	0.269225i
$357$		0			0
$358$	−0.272996	−	1.54824i	−0.0144283	−	0.0818268i
$359$	−2.47257	−	4.28262i	−0.130497	−	0.226028i	0.793371	−	0.608738i	$-0.208324\pi$
$359$	−2.47257	−	4.28262i	−0.130497	−	0.226028i	−0.923868	+	0.382710i	$0.874991\pi$
$360$		0			0
$361$	9.31282	−	16.1303i	0.490149	−	0.848962i
$362$	−1.15907	−	0.421865i	−0.0609191	−	0.0221728i
$363$		0			0
$364$	3.50054	+	2.93730i	0.183478	+	0.153956i
$365$	12.3066	+	10.3265i	0.644158	+	0.540513i
$366$		0			0
$367$	2.34214	+	0.852469i	0.122259	+	0.0444985i	0.402425	−	0.915453i	$-0.368167\pi$
$367$	2.34214	+	0.852469i	0.122259	+	0.0444985i	−0.280166	+	0.959951i	$0.590390\pi$
$368$	12.4660	−	21.5918i	0.649837	−	1.12555i
$369$		0			0
$370$	1.60281	+	2.77615i	0.0833262	+	0.144325i
$371$	−4.65513	−	26.4006i	−0.241682	−	1.37065i
$372$		0			0
$373$	26.3561	−	9.59284i	1.36467	−	0.496698i	0.447173	−	0.894447i	$-0.352431\pi$
$373$	26.3561	−	9.59284i	1.36467	−	0.496698i	0.917494	+	0.397749i	$0.130209\pi$
$374$	0.345983	−	1.96217i	0.0178903	−	0.101461i
$375$		0			0
$376$	−0.582677	+	0.488924i	−0.0300493	+	0.0252143i
$377$	−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	$0.457857\pi$
$380$	3.45025	−	2.89510i	0.176994	−	0.148516i
$381$		0			0
$382$	0.359111	−	2.03662i	0.0183737	−	0.104202i
$383$	0.0419788	−	0.0152790i	0.00214502	−	0.000780722i	−0.340947	−	0.940082i	$-0.610748\pi$
$383$	0.0419788	−	0.0152790i	0.00214502	−	0.000780722i	0.343092	+	0.939302i	$0.388526\pi$
$384$		0			0
$385$	4.90111	+	27.7956i	0.249784	+	1.41659i
$386$	−0.767463	−	1.32928i	−0.0390628	−	0.0676588i
$387$		0			0
$388$	−0.934167	+	1.61802i	−0.0474251	+	0.0821427i
$389$	−19.7169	−	7.17636i	−0.999685	−	0.363856i	−0.210222	−	0.977654i	$-0.567419\pi$
$389$	−19.7169	−	7.17636i	−0.999685	−	0.363856i	−0.789463	+	0.613798i	$0.789641\pi$
$390$		0			0
$391$	23.1045	+	19.3870i	1.16844	+	0.980441i
$392$	1.15207	+	0.966701i	0.0581883	+	0.0488258i
$393$		0			0
$394$	−1.20249	−	0.437669i	−0.0605804	−	0.0220495i
$395$	22.0356	−	38.1668i	1.10873	−	1.92038i
$396$		0			0
$397$	0.00122821	+	0.00212731i	6.16419e−5	+	0.000106767i	0.866056	−	0.499947i	$-0.166647\pi$
$397$	0.00122821	+	0.00212731i	6.16419e−5	+	0.000106767i	−0.865995	+	0.500053i	$0.833314\pi$
$398$	0.311896	+	1.76885i	0.0156339	+	0.0886645i
$399$		0			0
$400$	−32.1814	+	11.7131i	−1.60907	+	0.585654i
$401$	4.38571	−	24.8726i	0.219012	−	1.24208i	−0.654795	−	0.755807i	$-0.727245\pi$
$401$	4.38571	−	24.8726i	0.219012	−	1.24208i	0.873807	−	0.486273i	$-0.161644\pi$
$402$		0			0
$403$	−3.83940	+	3.22164i	−0.191254	+	0.160481i
$404$	−11.0485			−0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	9.46680	−	7.94359i	0.469252	−	0.393749i
$408$		0			0
$409$	−4.04401	+	22.9347i	−0.199964	+	1.13405i	0.705207	+	0.709001i	$0.250854\pi$
$409$	−4.04401	+	22.9347i	−0.199964	+	1.13405i	−0.905171	+	0.425048i	$0.860257\pi$
$410$	−3.19484	+	1.16283i	−0.157782	+	0.0574279i
$411$		0			0
$412$	3.22431	+	18.2859i	0.158850	+	0.900884i
$413$	−17.9643	−	31.1151i	−0.883965	−	1.53107i
$414$		0			0
$415$	16.8446	−	29.1756i	0.826867	−	1.43218i
$416$	−1.46277	−	0.532404i	−0.0717181	−	0.0261033i
$417$		0			0
$418$	0.202011	+	0.169507i	0.00988069	+	0.00829088i
$419$	23.9683	+	20.1118i	1.17093	+	0.982524i	0.999996	−	0.00275857i	$-0.000878081\pi$
$419$	23.9683	+	20.1118i	1.17093	+	0.982524i	0.170931	+	0.985283i	$0.445323\pi$
$420$		0			0
$421$	−28.6884	−	10.4417i	−1.39819	−	0.508899i	−0.470548	−	0.882374i	$-0.655944\pi$
$421$	−28.6884	−	10.4417i	−1.39819	−	0.508899i	−0.927640	+	0.373476i	$0.878166\pi$
$422$	1.80424	−	3.12503i	0.0878289	−	0.152124i
$423$		0			0
$424$	3.03640	+	5.25920i	0.147461	+	0.255409i
$425$	−7.19406	−	40.7995i	−0.348963	−	1.97907i
$426$		0			0
$427$	−23.3221	+	8.48856i	−1.12864	+	0.410790i
$428$	−0.437289	+	2.47999i	−0.0211372	+	0.119875i
$429$		0			0
$430$	−2.75811	+	2.31433i	−0.133008	+	0.111607i
$431$	12.4246			0.598474			0.299237	−	0.954179i	$-0.403268\pi$
$431$	12.4246			0.598474			0.299237	+	0.954179i	$0.403268\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	−2.63128	+	2.20790i	−0.126305	+	0.105983i
$435$		0			0
$436$	2.53390	−	14.3705i	0.121352	−	0.688221i
$437$	−3.75116	+	1.36531i	−0.179442	+	0.0653116i
$438$		0			0
$439$	5.22844	+	29.6519i	0.249540	+	1.41521i	0.809709	+	0.586831i	$0.199625\pi$
$439$	5.22844	+	29.6519i	0.249540	+	1.41521i	−0.560170	+	0.828378i	$0.689264\pi$
$440$	−3.19685	−	5.53711i	−0.152404	−	0.263971i
$441$		0			0
$442$	0.305914	−	0.529859i	0.0145508	−	0.0252028i
$443$	12.8377	+	4.67254i	0.609937	+	0.221999i	0.628476	−	0.777829i	$-0.283679\pi$
$443$	12.8377	+	4.67254i	0.609937	+	0.221999i	−0.0185388	+	0.999828i	$0.505901\pi$
$444$		0			0
$445$	−21.5790	−	18.1069i	−1.02294	−	0.858351i
$446$	−3.12432	−	2.62162i	−0.147941	−	0.124137i
$447$		0			0
$448$	20.7692	+	7.55937i	0.981253	+	0.357147i
$449$	−10.9995	+	19.0516i	−0.519097	+	0.899102i	0.480657	+	0.876909i	$0.340398\pi$
$449$	−10.9995	+	19.0516i	−0.519097	+	0.899102i	−0.999754	+	0.0221934i	$0.992935\pi$
$450$		0			0
$451$	6.55346	+	11.3509i	0.308590	+	0.534494i
$452$	3.19931	+	18.1442i	0.150483	+	0.853432i
$453$		0			0
$454$	1.70413	−	0.620254i	0.0799790	−	0.0291100i
$455$	−1.50501	+	8.53535i	−0.0705560	+	0.400143i
$456$		0			0
$457$	−1.14051	+	0.957000i	−0.0533507	+	0.0447666i	−0.669073	−	0.743197i	$-0.733309\pi$
$457$	−1.14051	+	0.957000i	−0.0533507	+	0.0447666i	0.615722	+	0.787963i	$0.288864\pi$
$458$	2.40132			0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	5.44913	−	4.57236i	0.253791	−	0.212956i	−0.507011	−	0.861939i	$-0.669250\pi$
$461$	5.44913	−	4.57236i	0.253791	−	0.212956i	0.760803	+	0.648983i	$0.224805\pi$
$462$		0			0
$463$	−4.60875	+	26.1375i	−0.214187	+	1.21471i	0.668125	+	0.744049i	$0.267097\pi$
$463$	−4.60875	+	26.1375i	−0.214187	+	1.21471i	−0.882312	+	0.470665i	$0.844014\pi$
$464$	−23.5237	+	8.56192i	−1.09206	+	0.397477i
$465$		0			0
$466$	0.228270	+	1.29458i	0.0105744	+	0.0599705i
$467$	13.0760	+	22.6482i	0.605084	+	1.04804i	0.992038	+	0.125937i	$0.0401937\pi$
$467$	13.0760	+	22.6482i	0.605084	+	1.04804i	−0.386955	+	0.922099i	$0.626473\pi$
$468$		0			0
$469$	1.83760	−	3.18282i	0.0848525	−	0.146969i
$470$	−0.672718	−	0.244849i	−0.0310302	−	0.0112941i
$471$		0			0
$472$	6.23479	+	5.23161i	0.286979	+	0.240804i
$473$	10.6328	+	8.92201i	0.488898	+	0.410234i
$474$		0			0
$475$	5.15260	+	1.87539i	0.236418	+	0.0860490i
$476$	−13.8043	+	23.9098i	−0.632719	+	1.09590i
$477$		0			0
$478$	−1.43213	−	2.48052i	−0.0655040	−	0.113456i
$479$	1.80708	+	10.2485i	0.0825675	+	0.468264i	0.997855	+	0.0654625i	$0.0208523\pi$
$479$	1.80708	+	10.2485i	0.0825675	+	0.468264i	−0.915288	+	0.402801i	$0.868037\pi$
$480$		0			0
$481$	3.56599	−	1.29791i	0.162595	−	0.0591798i
$482$	0.436091	−	2.47320i	0.0198634	−	0.112651i
$483$		0			0
$484$	7.23111	−	6.06762i	0.328687	−	0.275801i
$485$	−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	$0.637407\pi$
$488$	4.30689	−	3.61391i	0.194964	−	0.163594i
$489$		0			0
$490$	−0.245792	+	1.39396i	−0.0111038	+	0.0629725i
$491$	−15.9502	+	5.80541i	−0.719824	+	0.261995i	−0.675851	−	0.737038i	$-0.736224\pi$
$491$	−15.9502	+	5.80541i	−0.719824	+	0.261995i	−0.0439731	+	0.999033i	$0.514002\pi$
$492$		0			0
$493$	−5.25865	−	29.8233i	−0.236838	−	1.34317i
$494$	0.0404890	+	0.0701289i	0.00182168	+	0.00315525i
$495$		0			0
$496$	−12.5158	+	21.6780i	−0.561976	+	0.973371i
$497$	−14.0140	−	5.10066i	−0.628612	−	0.228796i
$498$		0			0
$499$	18.8801	+	15.8423i	0.845188	+	0.709197i	0.958724	−	0.284337i	$-0.0917735\pi$
$499$	18.8801	+	15.8423i	0.845188	+	0.709197i	−0.113537	+	0.993534i	$0.536218\pi$
$500$	−22.3416	−	18.7468i	−0.999145	−	0.838382i
$501$		0			0
$502$	−1.47132	−	0.535517i	−0.0656682	−	0.0239013i
$503$	20.0569	−	34.7395i	0.894291	−	1.54896i	0.0596120	−	0.998222i	$-0.481014\pi$
$503$	20.0569	−	34.7395i	0.894291	−	1.54896i	0.834679	−	0.550736i	$-0.185653\pi$
$504$		0			0
$505$	−10.4776	−	18.1478i	−0.466248	−	0.807564i
$506$	0.488304	+	2.76931i	0.0217077	+	0.123111i
$507$		0			0
$508$	38.5005	−	14.0130i	1.70818	−	0.621728i
$509$	−0.859301	+	4.87334i	−0.0380879	+	0.216007i	−0.997911	−	0.0645972i	$-0.979424\pi$
$509$	−0.859301	+	4.87334i	−0.0380879	+	0.216007i	0.959824	+	0.280604i	$0.0905348\pi$
$510$		0			0
$511$	9.98445	−	8.37795i	0.441686	−	0.370619i
$512$	−13.0229			−0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	−26.9779	+	22.6372i	−1.18879	+	0.997513i
$516$		0			0
$517$	−0.479242	+	2.71791i	−0.0210770	+	0.119534i
$518$	2.44390	−	0.889506i	0.107379	−	0.0390827i
$519$		0			0
$520$	−0.340932	−	1.93352i	−0.0149508	−	0.0847905i
$521$	3.86979	+	6.70267i	0.169539	+	0.293649i	0.938258	−	0.345937i	$-0.112439\pi$
$521$	3.86979	+	6.70267i	0.169539	+	0.293649i	−0.768719	+	0.639586i	$0.779106\pi$
$522$		0			0
$523$	−18.0070	+	31.1891i	−0.787391	+	1.36380i	0.140169	+	0.990128i	$0.455236\pi$
$523$	−18.0070	+	31.1891i	−0.787391	+	1.36380i	−0.927560	+	0.373674i	$0.878098\pi$
$524$	1.21412	+	0.441903i	0.0530390	+	0.0193046i
$525$		0			0
$526$	−3.55851	−	2.98595i	−0.155159	−	0.130194i
$527$	−23.1967	−	19.4644i	−1.01047	−	0.847882i
$528$		0			0
$529$	−18.3874	−	6.69247i	−0.799453	−	0.290977i
$530$	−2.85780	+	4.94986i	−0.124135	+	0.215008i
$531$		0			0
$532$	−1.82705	−	3.16455i	−0.0792129	−	0.137201i
$533$	0.698901	+	3.96367i	0.0302728	+	0.171685i
$534$		0			0
$535$	−4.48820	+	1.63357i	−0.194042	+	0.0706255i
$536$	−0.144570	+	0.819899i	−0.00624448	+	0.0354142i
$537$		0			0
$538$	1.55548	−	1.30520i	0.0670615	−	0.0562713i
$539$	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	$0.675873\pi$
$542$	−0.0191574	+	0.0160750i	−0.000822881	+	0.000690479i
$543$		0			0
$544$	1.63314	−	9.26199i	0.0700203	−	0.397105i
$545$	26.0072	−	9.46585i	1.11403	−	0.405473i
$546$		0			0
$547$	−4.92497	−	27.9309i	−0.210577	−	1.19424i	−0.888420	−	0.459032i	$-0.848196\pi$
$547$	−4.92497	−	27.9309i	−0.210577	−	1.19424i	0.677843	−	0.735207i	$-0.262915\pi$
$548$	−8.45913	−	14.6516i	−0.361356	−	0.625887i
$549$		0			0
$550$	1.93130	−	3.34512i	0.0823511	−	0.142636i
$551$	3.76640	+	1.37086i	0.160454	+	0.0584006i
$552$		0			0
$553$	−27.3902	−	22.9831i	−1.16475	−	0.977340i
$554$	0.134419	+	0.112791i	0.00571090	+	0.00479201i
$555$		0			0
$556$	24.8924	+	9.06010i	1.05567	+	0.384234i
$557$	−18.4687	+	31.9887i	−0.782542	+	1.35540i	0.147914	+	0.989000i	$0.452744\pi$
$557$	−18.4687	+	31.9887i	−0.782542	+	1.35540i	−0.930456	+	0.366403i	$0.880589\pi$
$558$		0			0
$559$	2.13113	+	3.69123i	0.0901372	+	0.156122i
$560$	7.51656	+	42.6285i	0.317633	+	1.80138i
$561$		0			0
$562$	4.47475	−	1.62868i	0.188756	−	0.0687016i
$563$	−3.95491	+	22.4294i	−0.166680	+	0.945287i	0.780636	+	0.624986i	$0.214895\pi$
$563$	−3.95491	+	22.4294i	−0.166680	+	0.945287i	−0.947316	+	0.320301i	$0.896216\pi$
$564$		0			0
$565$	−26.7688	+	22.4617i	−1.12617	+	0.944971i
$566$	4.63625			0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	−23.6468	+	19.8421i	−0.991327	+	0.831822i	−0.985759	−	0.168162i	$-0.946217\pi$
$569$	−23.6468	+	19.8421i	−0.991327	+	0.831822i	−0.00556781	+	0.999984i	$0.501772\pi$
$570$		0			0
$571$	2.22626	−	12.6257i	0.0931659	−	0.528370i	−0.902128	−	0.431468i	$-0.857996\pi$
$571$	2.22626	−	12.6257i	0.0931659	−	0.528370i	0.995294	−	0.0969016i	$-0.0308932\pi$
$572$	−3.52943	+	1.28461i	−0.147573	+	0.0537122i
$573$		0			0
$574$	0.478981	+	2.71644i	0.0199923	+	0.113382i
$575$	29.2354	+	50.6372i	1.21920	+	2.11172i
$576$		0			0
$577$	11.7632	−	20.3745i	0.489708	−	0.848200i	−0.510222	−	0.860043i	$-0.670437\pi$
$577$	11.7632	−	20.3745i	0.489708	−	0.848200i	0.999930	+	0.0118433i	$0.00376992\pi$
$578$	0.710338	+	0.258542i	0.0295462	+	0.0107539i
$579$		0			0
$580$	−36.9411	−	30.9973i	−1.53390	−	1.28709i
$581$	−20.9377	−	17.5688i	−0.868641	−	0.728877i
$582$		0			0
$583$	20.7055	+	7.53618i	0.857533	+	0.312117i
$584$	−1.47628	+	2.55699i	−0.0610888	+	0.105809i
$585$		0			0
$586$	−1.61363	−	2.79489i	−0.0666584	−	0.115456i
$587$	−1.97741	−	11.2144i	−0.0816164	−	0.462870i	−0.998036	−	0.0626498i	$-0.980045\pi$
$587$	−1.97741	−	11.2144i	−0.0816164	−	0.462870i	0.916419	−	0.400220i	$-0.131066\pi$
$588$		0			0
$589$	3.76614	−	1.37076i	0.155181	−	0.0564812i
$590$	−1.33018	+	7.54383i	−0.0547627	+	0.310575i
$591$		0			0
$592$	14.5187	−	12.1826i	0.596715	−	0.500703i
$593$	37.7324			1.54948			0.774742	−	0.632277i	$-0.217880\pi$
$593$	37.7324			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	14.5213	−	12.1848i	0.594816	−	0.499110i
$597$		0			0
$598$	−0.149946	+	0.850386i	−0.00613175	+	0.0347749i
$599$	44.5021	−	16.1975i	1.81831	−	0.661810i	0.822669	−	0.568520i	$-0.192484\pi$
$599$	44.5021	−	16.1975i	1.81831	−	0.661810i	0.995639	−	0.0932901i	$-0.0297384\pi$
$600$		0			0
$601$	−5.40175	−	30.6348i	−0.220342	−	1.24962i	−0.871392	−	0.490587i	$-0.836782\pi$
$601$	−5.40175	−	30.6348i	−0.220342	−	1.24962i	0.651050	−	0.759035i	$-0.274329\pi$
$602$	1.46054	+	2.52973i	0.0595271	+	0.103104i
$603$		0			0
$604$	−7.02156	+	12.1617i	−0.285703	+	0.494853i
$605$	16.8238	+	6.12338i	0.683986	+	0.248951i
$606$		0			0
$607$	22.5879	+	18.9535i	0.916815	+	0.769300i	0.973403	−	0.229098i	$-0.0735777\pi$
$607$	22.5879	+	18.9535i	0.916815	+	0.769300i	−0.0565879	+	0.998398i	$0.518022\pi$
$608$	0.953551	+	0.800125i	0.0386716	+	0.0324493i
$609$		0			0
$610$	4.97243	+	1.80982i	0.201328	+	0.0732773i
$611$	−0.423740	+	0.733939i	−0.0171427	+	0.0296920i
$612$		0			0
$613$	3.05214	+	5.28646i	0.123275	+	0.213518i	0.921057	−	0.389427i	$-0.127327\pi$
$613$	3.05214	+	5.28646i	0.123275	+	0.213518i	−0.797782	+	0.602945i	$0.793994\pi$
$614$	−1.01493	−	5.75593i	−0.0409591	−	0.232291i
$615$		0			0
$616$	−4.87442	+	1.77414i	−0.196396	+	0.0714823i
$617$	3.32017	−	18.8296i	0.133665	−	0.758052i	−0.842115	−	0.539298i	$-0.818690\pi$
$617$	3.32017	−	18.8296i	0.133665	−	0.758052i	0.975780	−	0.218754i	$-0.0701993\pi$
$618$		0			0
$619$	−5.17375	+	4.34129i	−0.207951	+	0.174491i	−0.740814	−	0.671710i	$-0.765560\pi$
$619$	−5.17375	+	4.34129i	−0.207951	+	0.174491i	0.532864	+	0.846201i	$0.321116\pi$
$620$	−48.2198			−1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	−17.5072	+	14.6903i	−0.701411	+	0.588553i
$624$		0			0
$625$	1.82437	−	10.3465i	0.0729749	−	0.413861i
$626$	0.542959	−	0.197621i	0.0217010	−	0.00789853i
$627$		0			0
$628$	−2.62931	−	14.9115i	−0.104921	−	0.595035i
$629$	11.4638	+	19.8559i	0.457091	+	0.791705i
$630$		0			0
$631$	0.228453	−	0.395693i	0.00909458	−	0.0157523i	−0.861442	−	0.507855i	$-0.830438\pi$
$631$	0.228453	−	0.395693i	0.00909458	−	0.0157523i	0.870537	+	0.492103i	$0.163772\pi$
$632$	7.61122	+	2.77026i	0.302758	+	0.110195i
$633$		0			0
$634$	4.11207	+	3.45044i	0.163311	+	0.137034i
$635$	59.5282	+	49.9501i	2.36231	+	1.98221i
$636$		0			0
$637$	1.57458	+	0.573102i	0.0623873	+	0.0227071i
$638$	1.41173	−	2.44519i	0.0558909	−	0.0968058i
$639$		0			0
$640$	−9.95805	−	17.2479i	−0.393627	−	0.681781i
$641$	−0.498549	−	2.82741i	−0.0196915	−	0.111676i	0.973378	−	0.229207i	$-0.0736132\pi$
$641$	−0.498549	−	2.82741i	−0.0196915	−	0.111676i	−0.993069	+	0.117531i	$0.962502\pi$
$642$		0			0
$643$	1.60015	−	0.582407i	0.0631037	−	0.0229679i	−0.310275	−	0.950647i	$-0.600421\pi$
$643$	1.60015	−	0.582407i	0.0631037	−	0.0229679i	0.373379	+	0.927679i	$0.378199\pi$
$644$	6.76628	−	38.3735i	0.266629	−	1.51213i
$645$		0			0
$646$	−0.374786	+	0.314483i	−0.0147458	+	0.0123732i
$647$	36.1004			1.41925			0.709626	−	0.704579i	$-0.248864\pi$
$647$	36.1004			1.41925			0.709626	+	0.704579i	$0.248864\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	0.908615	−	0.762419i	0.0356388	−	0.0299045i
$651$		0			0
$652$	−0.358350	+	2.03231i	−0.0140341	+	0.0795912i
$653$	40.9405	−	14.9011i	1.60213	−	0.583126i	0.622265	−	0.782807i	$-0.286213\pi$
$653$	40.9405	−	14.9011i	1.60213	−	0.583126i	0.979861	+	0.199681i	$0.0639905\pi$
$654$		0			0
$655$	0.425533	+	2.41332i	0.0166270	+	0.0942962i
$656$	10.0507	+	17.4083i	0.392412	+	0.679678i
$657$		0			0
$658$	−0.290404	+	0.502994i	−0.0113211	+	0.0196087i
$659$	−23.9443	−	8.71501i	−0.932737	−	0.339489i	−0.169443	−	0.985540i	$-0.554197\pi$
$659$	−23.9443	−	8.71501i	−0.932737	−	0.339489i	−0.763294	+	0.646051i	$0.776419\pi$
$660$		0			0
$661$	26.1736	+	21.9623i	1.01803	+	0.854233i	0.989379	−	0.145357i	$-0.0464330\pi$
$661$	26.1736	+	21.9623i	1.01803	+	0.854233i	0.0286555	+	0.999589i	$0.490877\pi$
$662$	−0.433521	−	0.363767i	−0.0168493	−	0.0141382i
$663$		0			0
$664$	5.81819	+	2.11765i	0.225790	+	0.0821807i
$665$	3.46529	−	6.00207i	0.134378	−	0.232750i
$666$		0			0
$667$	21.3702	+	37.0143i	0.827459	+	1.43320i
$668$	2.85794	+	16.2082i	0.110577	+	0.627112i
$669$		0			0
$670$	−0.736322	+	0.267999i	−0.0284466	+	0.0103537i
$671$	3.54234	−	20.0896i	0.136751	−	0.775551i
$672$		0			0
$673$	−22.6318	+	18.9903i	−0.872392	+	0.732024i	−0.964600	−	0.263716i	$-0.915052\pi$
$673$	−22.6318	+	18.9903i	−0.872392	+	0.732024i	0.0922084	+	0.995740i	$0.470607\pi$
$674$	−1.10113			−0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	31.2395	−	26.2130i	1.20063	−	1.00745i	0.201019	−	0.979587i	$-0.435575\pi$
$677$	31.2395	−	26.2130i	1.20063	−	1.00745i	0.999612	−	0.0278613i	$-0.00886968\pi$
$678$		0			0
$679$	−0.499227	+	2.83126i	−0.0191586	+	0.108654i
$680$	11.1467	−	4.05707i	0.427457	−	0.155581i
$681$		0			0
$682$	−0.490253	−	2.78036i	−0.0187728	−	0.106466i
$683$	−15.8213	−	27.4033i	−0.605384	−	1.04856i	−0.991991	−	0.126312i	$-0.959686\pi$
$683$	−15.8213	−	27.4033i	−0.605384	−	1.04856i	0.386606	−	0.922245i	$-0.373647\pi$
$684$		0			0
$685$	16.0441	−	27.7891i	0.613012	−	1.06177i
$686$	−2.37015	−	0.862664i	−0.0904927	−	0.0329367i
$687$		0			0
$688$	16.3070	+	13.6832i	0.621697	+	0.521666i
$689$	5.18321	+	4.34923i	0.197464	+	0.165692i
$690$		0			0
$691$	26.8609	+	9.77656i	1.02184	+	0.371918i	0.797967	−	0.602701i	$-0.205909\pi$
$691$	26.8609	+	9.77656i	1.02184	+	0.371918i	0.223869	+	0.974619i	$0.428131\pi$
$692$	−21.5190	+	37.2719i	−0.818028	+	1.41687i
$693$		0			0
$694$	−0.760438	−	1.31712i	−0.0288658	−	0.0499971i
$695$	8.72449	+	49.4791i	0.330939	+	1.87685i
$696$		0			0
$697$	−22.8505	+	8.31688i	−0.865523	+	0.315024i
$698$	−0.432539	+	2.45305i	−0.0163718	+	0.0928493i
$699$		0			0
$700$	−41.0011	+	34.4040i	−1.54969	+	1.30035i
$701$	−7.52982			−0.284397			−0.142199	−	0.989838i	$-0.545417\pi$
$701$	−7.52982			−0.284397			−0.142199	+	0.989838i	$0.545417\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	−13.9164	+	11.6772i	−0.524493	+	0.440102i
$705$		0			0
$706$	−0.997241	+	5.65564i	−0.0375317	+	0.212853i
$707$	−15.9758	+	5.81472i	−0.600832	+	0.218685i
$708$		0			0
$709$	1.39161	+	7.89224i	0.0522632	+	0.296399i	0.999725	−	0.0234711i	$-0.00747176\pi$
$709$	1.39161	+	7.89224i	0.0522632	+	0.296399i	−0.947461	+	0.319870i	$0.896361\pi$
$710$	1.58981	+	2.75363i	0.0596646	+	0.103342i
$711$		0			0
$712$	2.58857	−	4.48354i	0.0970108	−	0.168028i
$713$	40.1601	+	14.6171i	1.50401	+	0.547413i
$714$		0			0
$715$	−5.45709	−	4.57905i	−0.204084	−	0.171247i
$716$	−13.7163	−	11.5094i	−0.512603	−	0.430125i
$717$		0			0
$718$	0.803805	+	0.292561i	0.0299977	+	0.0109183i
$719$	−13.4913	+	23.3676i	−0.503140	+	0.871464i	0.496854	+	0.867834i	$0.334489\pi$
$719$	−13.4913	+	23.3676i	−0.503140	+	0.871464i	−0.999993	+	0.00362928i	$0.998845\pi$
$720$		0			0
$721$	14.2860	+	24.7440i	0.532037	+	0.921515i
$722$	0.559458	+	3.17284i	0.0208209	+	0.118081i
$723$		0			0
$724$	−13.2010	+	4.80476i	−0.490610	+	0.178568i
$725$	10.1946	−	57.8165i	0.378618	−	2.14725i
$726$		0			0
$727$	−11.2565	+	9.44534i	−0.417481	+	0.350308i	−0.827204	−	0.561902i	$-0.810070\pi$
$727$	−11.2565	+	9.44534i	−0.417481	+	0.350308i	0.409723	+	0.912210i	$0.365625\pi$
$728$	−1.59288			−0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	−19.7268	+	16.5528i	−0.729623	+	0.612227i
$732$		0			0
$733$	−5.44279	+	30.8676i	−0.201034	+	1.14012i	0.702526	+	0.711658i	$0.252056\pi$
$733$	−5.44279	+	30.8676i	−0.201034	+	1.14012i	−0.903560	+	0.428462i	$0.859056\pi$
$734$	−0.405134	+	0.147457i	−0.0149538	+	0.00544272i
$735$		0			0
$736$	2.30494	+	13.0719i	0.0849610	+	0.481838i
$737$	1.51039	+	2.61607i	0.0556359	+	0.0963642i
$738$		0			0
$739$	−0.241454	+	0.418211i	−0.00888205	+	0.0153842i	−0.870432	−	0.492288i	$-0.836161\pi$
$739$	−0.241454	+	0.418211i	−0.00888205	+	0.0153842i	0.861550	+	0.507672i	$0.169494\pi$
$740$	34.3081	+	12.4871i	1.26119	+	0.459035i
$741$		0			0
$742$	3.55223	+	2.98068i	0.130407	+	0.109424i
$743$	32.9788	+	27.6725i	1.20987	+	1.01520i	0.999292	+	0.0376288i	$0.0119804\pi$
$743$	32.9788	+	27.6725i	1.20987	+	1.01520i	0.210582	+	0.977576i	$0.432464\pi$
$744$		0			0
$745$	33.7852	+	12.2968i	1.23779	+	0.450520i
$746$	−2.42578	+	4.20157i	−0.0888140	+	0.153830i
$747$		0			0
$748$	−11.3462	−	19.6523i	−0.414860	−	0.718558i
$749$	0.672887	+	3.81613i	0.0245867	+	0.139438i
$750$		0			0
$751$	−41.2728	+	15.0221i	−1.50607	+	0.548163i	−0.957623	−	0.288024i	$-0.907002\pi$
$751$	−41.2728	+	15.0221i	−1.50607	+	0.548163i	−0.548443	+	0.836188i	$0.684779\pi$
$752$	−0.734985	+	4.16831i	−0.0268022	+	0.152003i
$753$		0			0
$754$	0.664172	−	0.557306i	0.0241877	−	0.0202959i
$755$	−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	$0.366460\pi$
$758$	−0.681075	+	0.571490i	−0.0247378	+	0.0207575i
$759$		0			0
$760$	−0.272626	+	1.54614i	−0.00988920	+	0.0560844i
$761$	9.39386	−	3.41909i	0.340527	−	0.123942i	−0.166095	−	0.986110i	$-0.553116\pi$
$761$	9.39386	−	3.41909i	0.340527	−	0.123942i	0.506623	+	0.862168i	$0.330894\pi$
$762$		0			0
$763$	−3.89909	−	22.1128i	−0.141157	−	0.800538i
$764$	−11.7768	−	20.3980i	−0.426069	−	0.737972i
$765$		0			0
$766$	−0.00386367	+	0.00669207i	−0.000139600	+	0.000241794i
$767$	8.52136	+	3.10152i	0.307688	+	0.111989i
$768$		0			0
$769$	−5.74242	−	4.81846i	−0.207077	−	0.173758i	0.533351	−	0.845894i	$-0.320933\pi$
$769$	−5.74242	−	4.81846i	−0.207077	−	0.173758i	−0.740428	+	0.672136i	$0.765377\pi$
$770$	−3.73994	−	3.13818i	−0.134778	−	0.113092i
$771$		0			0
$772$	−16.4275	−	5.97912i	−0.591238	−	0.215193i
$773$	9.91954	−	17.1812i	0.356781	−	0.617963i	−0.630640	−	0.776076i	$-0.717207\pi$
$773$	9.91954	−	17.1812i	0.356781	−	0.617963i	0.987421	+	0.158112i	$0.0505408\pi$
$774$		0			0
$775$	−29.3521	−	50.8394i	−1.05436	−	1.82620i
$776$	−0.113090	−	0.641367i	−0.00405971	−	0.0230237i
$777$		0			0
$778$	3.41055	−	1.24134i	0.122274	−	0.0445041i
$779$	0.558877	−	3.16955i	0.0200239	−	0.113561i
$780$		0			0
$781$	9.39002	−	7.87917i	0.336001	−	0.281939i
$782$	−5.21709			−0.186563
$783$		0			0
$784$	8.36872			0.298883
$785$	21.9995	−	18.4598i	0.785197	−	0.658859i
$786$		0			0
$787$	6.89874	−	39.1247i	0.245913	−	1.39464i	−0.572448	−	0.819941i	$-0.694006\pi$
$787$	6.89874	−	39.1247i	0.245913	−	1.39464i	0.818362	−	0.574704i	$-0.194883\pi$
$788$	−13.6955	+	4.98476i	−0.487882	+	0.177575i
$789$		0			0
$790$	1.32377	+	7.50746i	0.0470975	+	0.267103i
$791$	14.1752	+	24.5522i	0.504013	+	0.872976i
$792$		0			0
$793$	3.13210	−	5.42495i	0.111224	−	0.192646i
$794$	−0.000399275	0	0.000145324i	−1.41698e−5	0	5.15737e-6i
$795$		0			0
$796$	15.6708	+	13.1494i	0.555438	+	0.466068i
$797$	−6.97556	−	5.85319i	−0.247087	−	0.207331i	0.510830	−	0.859682i	$-0.329338\pi$
$797$	−6.97556	−	5.85319i	−0.247087	−	0.207331i	−0.757917	+	0.652351i	$0.773783\pi$
$798$		0			0
$799$	−4.81148	−	1.75123i	−0.170218	−	0.0619542i
$800$	9.11632	−	15.7899i	0.322311	−	0.558258i
$801$		0			0
$802$	2.18437	+	3.78344i	0.0771327	+	0.133598i
$803$	1.86028	+	10.5502i	0.0656478	+	0.372307i
$804$		0			0
$805$	69.4471	−	25.2767i	2.44769	−	0.890886i
$806$	0.150545	−	0.853782i	0.00530271	−	0.0300732i
$807$		0			0
$808$	2.95025	−	2.47555i	0.103789	−	0.0870897i
$809$	3.01910			0.106146			0.0530730	−	0.998591i	$-0.483098\pi$
$809$	3.01910			0.106146			0.0530730	+	0.998591i	$0.483098\pi$
$810$		0			0
$811$	33.1722			1.16483			0.582416	−	0.812891i	$-0.302107\pi$
$811$	33.1722			1.16483			0.582416	+	0.812891i	$0.302107\pi$
$812$	−29.9706	+	25.1483i	−1.05176	+	0.882533i
$813$		0			0
$814$	−0.371198	+	2.10517i	−0.0130105	+	0.0737861i
$815$	−3.67800	+	1.33868i	−0.128835	+	0.0468920i
$816$		0			0
$817$	−0.591849	−	3.35654i	−0.0207062	−	0.117431i
$818$	−2.01418	−	3.48866i	−0.0704241	−	0.121978i
$819$		0			0
$820$	−19.3612	+	33.5345i	−0.676121	+	1.17108i
$821$	−40.1831	−	14.6255i	−1.40240	−	0.510432i	−0.473510	−	0.880788i	$-0.657013\pi$
$821$	−40.1831	−	14.6255i	−1.40240	−	0.510432i	−0.928890	+	0.370357i	$0.879235\pi$
$822$		0			0
$823$	−26.9869	−	22.6447i	−0.940703	−	0.789344i	0.0370044	−	0.999315i	$-0.488218\pi$
$823$	−26.9869	−	22.6447i	−0.940703	−	0.789344i	−0.977708	+	0.209971i	$0.932663\pi$
$824$	−4.95817	−	4.16040i	−0.172726	−	0.144934i
$825$		0			0
$826$	5.83998	+	2.12558i	0.203199	+	0.0739584i
$827$	−13.0190	+	22.5495i	−0.452714	+	0.784125i	−0.998554	−	0.0537655i	$-0.982878\pi$
$827$	−13.0190	+	22.5495i	−0.452714	+	0.784125i	0.545839	+	0.837890i	$0.316211\pi$
$828$		0			0
$829$	3.95134	+	6.84392i	0.137236	+	0.237699i	0.926449	−	0.376420i	$-0.122845\pi$
$829$	3.95134	+	6.84392i	0.137236	+	0.237699i	−0.789214	+	0.614119i	$0.789512\pi$
$830$	1.01192	+	5.73888i	0.0351242	+	0.199199i
$831$		0			0
$832$	−5.24207	+	1.90796i	−0.181736	+	0.0661465i
$833$	−1.75798	+	9.96999i	−0.0609103	+	0.345440i
$834$		0			0
$835$	−23.9125	+	20.0650i	−0.827526	+	0.694376i
$836$	3.00344			0.103876
$837$		0			0
$838$	−5.41213			−0.186959
$839$	3.94390	−	3.30932i	0.136158	−	0.114250i	−0.572165	−	0.820139i	$-0.693896\pi$
$839$	3.94390	−	3.30932i	0.136158	−	0.114250i	0.708323	+	0.705888i	$0.249452\pi$
$840$		0			0
$841$	2.41617	−	13.7028i	0.0833163	−	0.472510i
$842$	4.96241	−	1.80617i	0.171016	−	0.0622447i
$843$		0			0
$844$	−7.13661	−	40.4737i	−0.245652	−	1.39316i
$845$	23.1939	+	40.1730i	0.797894	+	1.38199i
$846$		0			0
$847$	7.26264	−	12.5793i	0.249547	−	0.432228i
$848$	31.7548	+	11.5578i	1.09046	+	0.396897i
$849$		0			0
$850$	5.48963	+	4.60635i	0.188293	+	0.157996i
$851$	−24.7883	−	20.7999i	−0.849733	−	0.713011i
$852$		0			0
$853$	−24.4230	−	8.88926i	−0.836229	−	0.304362i	−0.111816	−	0.993729i	$-0.535667\pi$
$853$	−24.4230	−	8.88926i	−0.836229	−	0.304362i	−0.724413	+	0.689366i	$0.757889\pi$
$854$	2.14653	−	3.71791i	0.0734529	−	0.127224i
$855$		0			0
$856$	−0.438904	−	0.760204i	−0.0150014	−	0.0259832i
$857$	−0.715280	−	4.05656i	−0.0244335	−	0.138569i	0.970151	−	0.242503i	$-0.0779683\pi$
$857$	−0.715280	−	4.05656i	−0.0244335	−	0.138569i	−0.994584	+	0.103933i	$0.966857\pi$
$858$		0			0
$859$	6.04168	−	2.19899i	0.206140	−	0.0750287i	−0.236887	−	0.971537i	$-0.576127\pi$
$859$	6.04168	−	2.19899i	0.206140	−	0.0750287i	0.443026	+	0.896509i	$0.353905\pi$
$860$	−7.12076	+	40.3838i	−0.242816	+	1.37708i
$861$		0			0
$862$	−1.64636	+	1.38146i	−0.0560751	+	0.0470526i
$863$	29.6195			1.00826			0.504129	−	0.863628i	$-0.331813\pi$
$863$	29.6195			1.00826			0.504129	+	0.863628i	$0.331813\pi$
$864$		0			0
$865$	−81.6282			−2.77544
$866$	0.100792	−	0.0845742i	0.00342504	−	0.00287395i
$867$		0			0
$868$	−6.79330	+	38.5267i	−0.230580	+	1.30768i
$869$	27.6162	−	10.0515i	0.936816	−	0.340973i
$870$		0			0
$871$	0.161077	+	0.913514i	0.00545789	+	0.0309533i
$872$	2.54326	+	4.40505i	0.0861256	+	0.149174i
$873$		0			0
$874$	0.345251	−	0.597993i	0.0116783	−	0.0202274i
$875$	−42.1715	−	15.3492i	−1.42566	−	0.518896i
$876$		0			0
$877$	−24.4121	−	20.4842i	−0.824337	−	0.691701i	0.129647	−	0.991560i	$-0.458616\pi$
$877$	−24.4121	−	20.4842i	−0.824337	−	0.691701i	−0.953983	+	0.299860i	$0.903060\pi$
$878$	−3.98971	−	3.34776i	−0.134646	−	0.112982i
$879$		0			0
$880$	−33.4328	−	12.1685i	−1.12702	−	0.410201i
$881$	−17.3932	+	30.1259i	−0.585991	+	1.01497i	0.408760	+	0.912642i	$0.365961\pi$
$881$	−17.3932	+	30.1259i	−0.585991	+	1.01497i	−0.994751	+	0.102325i	$0.967372\pi$
$882$		0			0
$883$	15.1882	+	26.3067i	0.511124	+	0.885292i	0.999917	+	0.0128924i	$0.00410388\pi$
$883$	15.1882	+	26.3067i	0.511124	+	0.885292i	−0.488793	+	0.872400i	$0.662563\pi$
$884$	−1.21003	−	6.86244i	−0.0406979	−	0.230809i
$885$		0			0
$886$	−2.22061	+	0.808236i	−0.0746029	+	0.0271532i
$887$	−8.68721	+	49.2676i	−0.291688	+	1.65424i	0.388679	+	0.921373i	$0.372931\pi$
$887$	−8.68721	+	49.2676i	−0.291688	+	1.65424i	−0.680367	+	0.732871i	$0.738180\pi$
$888$		0			0
$889$	48.2957	−	40.5249i	1.61978	−	1.35916i
$890$	4.87263			0.163331
$891$		0			0
$892$	−46.4515			−1.55531
$893$	0.519139	−	0.435609i	0.0173723	−	0.0145771i
$894$		0			0
$895$	5.89715	−	33.4444i	0.197120	−	1.11792i
$896$	−15.1836	+	5.52638i	−0.507249	+	0.184624i
$897$		0			0
$898$	−0.660781	−	3.74747i	−0.0220505	−	0.125055i
$899$	−21.4556	−	37.1621i	−0.715583	−	1.23943i
$900$		0			0
$901$	−20.4399	+	35.4029i	−0.680950	+	1.17944i
$902$	−2.13045	−	0.775422i	−0.0709363	−	0.0258187i
$903$		0			0
$904$	−4.91973	−	4.12815i	−0.163628	−	0.137300i
$905$	−20.4109	−	17.1268i	−0.678482	−	0.569314i
$906$		0			0
$907$	41.4069	+	15.0709i	1.37489	+	0.500420i	0.920626	−	0.390445i	$-0.127679\pi$
$907$	41.4069	+	15.0709i	1.37489	+	0.500420i	0.454268	+	0.890865i	$0.349901\pi$
$908$	10.3273	−	17.8874i	0.342723	−	0.593614i
$909$		0			0
$910$	−0.749593	−	1.29833i	−0.0248488	−	0.0430393i
$911$	−6.45594	−	36.6134i	−0.213895	−	1.21306i	−0.882814	−	0.469723i	$-0.844354\pi$
$911$	−6.45594	−	36.6134i	−0.213895	−	1.21306i	0.668919	−	0.743335i	$-0.266757\pi$
$912$		0			0
$913$	21.1105	−	7.68359i	0.698655	−	0.254290i
$914$	0.0447198	−	0.253619i	0.00147920	−	0.00838896i
$915$		0			0
$916$	20.9509	−	17.5799i	0.692237	−	0.580856i
$917$	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	$0.434450\pi$
$920$	−12.8248	+	10.7613i	−0.422821	+	0.354789i
$921$		0			0
$922$	−0.213663	+	1.21174i	−0.00703662	+	0.0399066i
$923$	3.53707	−	1.28739i	0.116424	−	0.0423749i
$924$		0			0
$925$	7.71835	+	43.7730i	0.253778	+	1.43925i
$926$	−2.29545	−	3.97584i	−0.0754333	−	0.130654i
$927$		0			0
$928$	6.66377	−	11.5420i	0.218749	−	0.378884i
$929$	−31.3747	−	11.4194i	−1.02937	−	0.374660i	−0.228528	−	0.973537i	$-0.573391\pi$
$929$	−31.3747	−	11.4194i	−1.02937	−	0.374660i	−0.800841	+	0.598878i	$0.795614\pi$
$930$		0			0
$931$	−1.02644	−	0.861287i	−0.0336403	−	0.0282275i
$932$	11.4691	+	9.62375i	0.375684	+	0.315237i
$933$		0			0
$934$	−4.25085	−	1.54718i	−0.139092	−	0.0506253i
$935$	21.5199	−	37.2736i	0.703777	−	1.21898i
$936$		0			0
$937$	12.4220	+	21.5156i	0.405810	+	0.702884i	0.994415	−	0.105537i	$-0.0336561\pi$
$937$	12.4220	+	21.5156i	0.405810	+	0.702884i	−0.588605	+	0.808421i	$0.700323\pi$
$938$	0.110392	+	0.626063i	0.00360442	+	0.0204417i
$939$		0			0
$940$	−7.66180	+	2.78867i	−0.249900	+	0.0909563i
$941$	4.41585	−	25.0435i	0.143953	−	0.816396i	−0.824249	−	0.566227i	$-0.808403\pi$
$941$	4.41585	−	25.0435i	0.143953	−	0.816396i	0.968202	−	0.250169i	$-0.0804863\pi$
$942$		0			0
$943$	26.2905	−	22.0603i	0.856136	−	0.718383i
$944$	45.2900			1.47406
$945$		0			0
$946$	−2.40094			−0.0780612
$947$	12.7394	−	10.6897i	0.413976	−	0.347367i	−0.411890	−	0.911234i	$-0.635131\pi$
$947$	12.7394	−	10.6897i	0.413976	−	0.347367i	0.825866	+	0.563866i	$0.190687\pi$
$948$		0			0
$949$	−0.571246	+	3.23970i	−0.0185434	+	0.105165i
$950$	−0.891276	+	0.324398i	−0.0289168	+	0.0105249i
$951$		0			0
$952$	−1.67115	−	9.47757i	−0.0541623	−	0.307170i
$953$	−7.13357	−	12.3557i	−0.231079	−	0.400240i	0.727047	−	0.686588i	$-0.240892\pi$
$953$	−7.13357	−	12.3557i	−0.231079	−	0.400240i	−0.958126	+	0.286347i	$0.907559\pi$
$954$		0			0
$955$	22.3365	−	38.6879i	0.722791	−	1.25191i
$956$	−30.6546	−	11.1574i	−0.991440	−	0.360855i
$957$		0			0
$958$	−1.37894	−	1.15707i	−0.0445516	−	0.0373833i
$959$	−19.9427	−	16.7339i	−0.643982	−	0.540365i
$960$		0			0
$961$	−11.1899	−	4.07280i	−0.360965	−	0.131381i
$962$	−0.328209	+	0.568474i	−0.0105819	+	0.0183283i
$963$		0			0
$964$	−14.3013	−	24.7706i	−0.460613	−	0.797806i
$965$	−5.75763	−	32.6532i	−0.185345	−	1.05114i
$966$		0			0
$967$	36.7277	−	13.3678i	1.18108	−	0.429879i	0.324498	−	0.945886i	$-0.394805\pi$
$967$	36.7277	−	13.3678i	1.18108	−	0.429879i	0.856584	+	0.516008i	$0.172582\pi$
$968$	−0.571376	+	3.24044i	−0.0183647	+	0.104152i
$969$		0			0
$970$	0.469551	−	0.394000i	0.0150764	−	0.0126506i
$971$	−4.40370			−0.141321			−0.0706607	−	0.997500i	$-0.522511\pi$
$971$	−4.40370			−0.141321			−0.0706607	+	0.997500i	$0.522511\pi$
$972$		0			0
$973$	40.7619			1.30677
$974$	2.44693	−	2.05322i	0.0784046	−	0.0657893i
$975$		0			0
$976$	5.43268	−	30.8103i	0.173896	−	0.986213i
$977$	−39.5860	+	14.4081i	−1.26647	+	0.460957i	−0.885935	−	0.463810i	$-0.846482\pi$
$977$	−39.5860	+	14.4081i	−1.26647	+	0.460957i	−0.380534	+	0.924767i	$0.624260\pi$
$978$		0			0
$979$	−3.26190	−	18.4991i	−0.104251	−	0.591235i
$980$	8.06057	+	13.9613i	0.257486	+	0.445978i
$981$		0			0
$982$	1.46804	−	2.54272i	0.0468470	−	0.0811413i
$983$	19.1943	+	6.98615i	0.612203	+	0.222824i	0.629467	−	0.777027i	$-0.283273\pi$
$983$	19.1943	+	6.98615i	0.612203	+	0.222824i	−0.0172640	+	0.999851i	$0.505496\pi$
$984$		0			0
$985$	−21.1756	−	17.7684i	−0.674709	−	0.566148i
$986$	4.01276	+	3.36711i	0.127792	+	0.107231i
$987$		0			0
$988$	0.866663	+	0.315440i	0.0275722	+	0.0100355i
$989$	18.1723	−	31.4753i	0.577844	−	1.00086i
$990$		0			0
$991$	−0.0340356	−	0.0589514i	−0.00108118	−	0.00187265i	0.865484	−	0.500936i	$-0.167011\pi$
$991$	−0.0340356	−	0.0589514i	−0.00108118	−	0.00187265i	−0.866565	+	0.499063i	$0.833677\pi$
$992$	−2.31414	−	13.1241i	−0.0734740	−	0.416691i
$993$		0			0
$994$	2.42408	−	0.882292i	0.0768871	−	0.0279846i
$995$	−6.73747	+	38.2101i	−0.213592	+	1.21134i
$996$		0			0
$997$	8.15539	−	6.84318i	0.258284	−	0.216726i	−0.504446	−	0.863443i	$-0.668303\pi$
$997$	8.15539	−	6.84318i	0.258284	−	0.216726i	0.762730	+	0.646718i	$0.223859\pi$
$998$	−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.u.325.1		12
3.2	odd	2		729.2.e.j.325.2		12
9.2	odd	6		729.2.e.t.568.1		12
9.4	even	3		729.2.e.l.82.1		12
9.5	odd	6		729.2.e.s.82.2		12
9.7	even	3		729.2.e.k.568.2		12
27.2	odd	18		729.2.e.t.163.1		12
27.4	even	9		729.2.a.e.1.3	yes	6
27.5	odd	18		729.2.c.d.244.3		12
27.7	even	9		729.2.e.l.649.1		12
27.11	odd	18		729.2.e.j.406.2		12
27.13	even	9		729.2.c.a.487.4		12
27.14	odd	18		729.2.c.d.487.3		12
27.16	even	9	inner	729.2.e.u.406.1		12
27.20	odd	18		729.2.e.s.649.2		12
27.22	even	9		729.2.c.a.244.4		12
27.23	odd	18		729.2.a.b.1.4	✓	6
27.25	even	9		729.2.e.k.163.2		12

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

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)

\(f(q)\)	\(=\)	\(q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +O(q^{10})\)	\(q+(-0.132507 + 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(-3.51122 + 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(-0.343364 - 0.594724i) q^{8} +(0.323168 - 0.559743i) q^{10} +(-2.34143 - 0.852210i) q^{11} +(-0.586130 - 0.491822i) q^{13} +(-0.401695 - 0.337062i) q^{14} +(-3.59091 - 1.30699i) q^{16} +(2.31139 - 4.00345i) q^{17} +(0.305922 + 0.529872i) q^{19} +(-1.27828 - 7.24949i) q^{20} +(0.405011 - 0.147412i) q^{22} +(-1.13295 + 6.42526i) q^{23} +(6.86521 - 5.76060i) q^{25} +0.132351 q^{26} -5.97229 q^{28} +(5.01827 - 4.21083i) q^{29} +(1.13747 - 6.45091i) q^{31} +(1.91177 - 0.695827i) q^{32} +(0.138854 + 0.787482i) q^{34} +(-5.66369 - 9.80980i) q^{35} +(-2.47984 + 4.29522i) q^{37} +(-0.0994517 - 0.0361975i) q^{38} +(1.96567 + 1.64939i) q^{40} +(-4.02958 - 3.38122i) q^{41} +(-5.23463 - 1.90525i) q^{43} +(2.45442 - 4.25118i) q^{44} +(-0.564280 - 0.977362i) q^{46} +(-0.192335 - 1.09079i) q^{47} +(-2.05791 + 0.749017i) q^{49} +(-0.269188 + 1.52664i) q^{50} +(1.15472 - 0.968928i) q^{52} -8.84310 q^{53} +9.31038 q^{55} +(1.59476 - 1.33816i) q^{56} +(-0.196769 + 1.11593i) q^{58} +(-11.1370 + 4.05354i) q^{59} +(1.42166 + 8.06263i) q^{61} +(0.566533 + 0.981264i) q^{62} +(3.64541 - 6.31404i) q^{64} +(2.68657 + 0.977832i) q^{65} +(-0.928705 - 0.779276i) q^{67} +(6.97656 + 5.85403i) q^{68} +(1.84120 + 0.670142i) q^{70} +(-2.45973 + 4.26038i) q^{71} +(-2.14972 - 3.72343i) q^{73} +(-0.148974 - 0.844873i) q^{74} +(-1.13269 + 0.412265i) q^{76} +(1.31166 - 7.43882i) q^{77} +(-9.03519 + 7.58143i) q^{79} +14.2788 q^{80} +0.909895 q^{82} +(-6.90671 + 5.79542i) q^{83} +(-2.99948 + 17.0109i) q^{85} +(0.905464 - 0.329562i) q^{86} +(0.297133 + 1.68512i) q^{88} +(3.76943 + 6.52884i) q^{89} +(1.15976 - 2.00876i) q^{91} +(-12.0784 - 4.39617i) q^{92} +(0.146767 + 0.123152i) q^{94} +(-1.75133 - 1.46954i) q^{95} +(0.891161 + 0.324356i) q^{97} +(0.189407 - 0.328062i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 3 * q^13 - 15 * q^14 - 36 * q^16 + 9 * q^17 - 12 * q^19 - 42 * q^20 + 6 * q^22 - 6 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 54 * q^32 - 9 * q^34 - 30 * q^35 - 3 * q^37 - 42 * q^38 - 57 * q^40 - 24 * q^41 + 6 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 + 33 * q^49 - 21 * q^50 + 45 * q^52 - 18 * q^53 + 30 * q^55 - 3 * q^56 + 33 * q^58 - 15 * q^59 + 33 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 + 42 * q^67 + 18 * q^68 + 24 * q^70 - 12 * q^73 + 3 * q^74 - 87 * q^76 + 57 * q^77 - 48 * q^79 - 42 * q^80 - 42 * q^82 - 12 * q^83 - 36 * q^85 + 30 * q^86 + 30 * q^88 + 9 * q^89 - 18 * q^91 + 48 * q^92 + 33 * q^94 - 30 * q^95 - 3 * q^97 - 18 * q^98

Introduction

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