LMFDB - Embedded newform 729.2.e.j.325.2

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			325.2
Root			$0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.j.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.132507 - 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(3.51122 - 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(0.343364 + 0.594724i) q^{8} +O(q^{10})$	\(q+(0.132507 - 0.111187i) q^{2} +(-0.342101 + 1.94015i) q^{4} +(3.51122 - 1.27798i) q^{5} +(0.526414 + 2.98544i) q^{7} +(0.343364 + 0.594724i) q^{8} +(0.323168 - 0.559743i) q^{10} +(2.34143 + 0.852210i) q^{11} +(-0.586130 - 0.491822i) q^{13} +(0.401695 + 0.337062i) q^{14} +(-3.59091 - 1.30699i) q^{16} +(-2.31139 + 4.00345i) q^{17} +(0.305922 + 0.529872i) q^{19} +(1.27828 + 7.24949i) q^{20} +(0.405011 - 0.147412i) q^{22} +(1.13295 - 6.42526i) q^{23} +(6.86521 - 5.76060i) q^{25} -0.132351 q^{26} -5.97229 q^{28} +(-5.01827 + 4.21083i) q^{29} +(1.13747 - 6.45091i) q^{31} +(-1.91177 + 0.695827i) q^{32} +(0.138854 + 0.787482i) q^{34} +(5.66369 + 9.80980i) q^{35} +(-2.47984 + 4.29522i) q^{37} +(0.0994517 + 0.0361975i) q^{38} +(1.96567 + 1.64939i) q^{40} +(4.02958 + 3.38122i) q^{41} +(-5.23463 - 1.90525i) q^{43} +(-2.45442 + 4.25118i) q^{44} +(-0.564280 - 0.977362i) q^{46} +(0.192335 + 1.09079i) q^{47} +(-2.05791 + 0.749017i) q^{49} +(0.269188 - 1.52664i) q^{50} +(1.15472 - 0.968928i) q^{52} +8.84310 q^{53} +9.31038 q^{55} +(-1.59476 + 1.33816i) q^{56} +(-0.196769 + 1.11593i) q^{58} +(11.1370 - 4.05354i) q^{59} +(1.42166 + 8.06263i) q^{61} +(-0.566533 - 0.981264i) q^{62} +(3.64541 - 6.31404i) q^{64} +(-2.68657 - 0.977832i) q^{65} +(-0.928705 - 0.779276i) q^{67} +(-6.97656 - 5.85403i) q^{68} +(1.84120 + 0.670142i) q^{70} +(2.45973 - 4.26038i) q^{71} +(-2.14972 - 3.72343i) q^{73} +(0.148974 + 0.844873i) q^{74} +(-1.13269 + 0.412265i) q^{76} +(-1.31166 + 7.43882i) q^{77} +(-9.03519 + 7.58143i) q^{79} -14.2788 q^{80} +0.909895 q^{82} +(6.90671 - 5.79542i) q^{83} +(-2.99948 + 17.0109i) q^{85} +(-0.905464 + 0.329562i) q^{86} +(0.297133 + 1.68512i) q^{88} +(-3.76943 - 6.52884i) q^{89} +(1.15976 - 2.00876i) q^{91} +(12.0784 + 4.39617i) q^{92} +(0.146767 + 0.123152i) q^{94} +(1.75133 + 1.46954i) q^{95} +(0.891161 + 0.324356i) q^{97} +(-0.189407 + 0.328062i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.594736	−	0.803921i	$-0.702743\pi$
$2$	0.132507	−	0.111187i	0.0936968	−	0.0786209i	0.688433	+	0.725300i	$0.258299\pi$
$3$		0			0
$3$		0			0
$4$	−0.342101	+	1.94015i	−0.171050	+	0.970075i
$5$	3.51122	−	1.27798i	1.57027	−	0.571530i	0.597207	−	0.802087i	$-0.296277\pi$
$5$	3.51122	−	1.27798i	1.57027	−	0.571530i	0.973059	+	0.230557i	$0.0740550\pi$
$6$		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	0.669957	−	0.742400i	$-0.266313\pi$
$11$	2.34143	+	0.852210i	0.705967	+	0.256951i	0.0360107	+	0.999351i	$0.488535\pi$
$12$		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	$0.356094\pi$
$17$	−2.31139	+	4.00345i	−0.560595	+	0.970979i	−0.997445	+	0.0714442i	$0.977239\pi$
$18$		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	$-0.706332\pi$
$23$	1.13295	−	6.42526i	0.236236	−	1.33976i	0.839996	−	0.542593i	$-0.182557\pi$
$24$		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	−0.976152	−	0.217087i	$-0.930344\pi$
$29$	−5.01827	+	4.21083i	−0.931870	+	0.781932i	0.0442820	+	0.999019i	$0.485900\pi$
$30$		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	0.900716	−	0.434409i	$-0.143043\pi$
$41$	4.02958	+	3.38122i	0.629314	+	0.528057i	−0.271402	+	0.962466i	$0.587487\pi$
$42$		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	0.995617	−	0.0935267i	$-0.0298141\pi$
$47$	0.192335	+	1.09079i	0.0280550	+	0.159108i	−0.967562	+	0.252635i	$0.918703\pi$
$48$		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	$-0.292234\pi$
$53$	8.84310			1.21469			0.607346	+	0.794437i	$0.292234\pi$
$54$		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	0.507347	−	0.861742i	$-0.330626\pi$
$59$	11.1370	−	4.05354i	1.44992	−	0.527726i	0.942568	+	0.334016i	$0.108404\pi$
$60$		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	−0.682346	−	0.731029i	$-0.739040\pi$
$71$	2.45973	−	4.26038i	0.291916	−	0.505614i	0.974263	+	0.225415i	$0.0723738\pi$
$72$		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	−0.179524	−	0.983754i	$-0.557456\pi$
$83$	6.90671	−	5.79542i	0.758110	−	0.636130i	0.937634	+	0.347624i	$0.113011\pi$
$84$		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	0.594113	−	0.804382i	$-0.297503\pi$
$89$	−3.76943	−	6.52884i	−0.399558	−	0.692055i	−0.993671	+	0.112326i	$0.964170\pi$
$90$		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	$-0.965547\pi$
$101$	−0.973846	−	5.52295i	−0.0969013	−	0.549554i	0.897247	−	0.441529i	$-0.145564\pi$
$102$		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	$-0.519680\pi$
$107$	−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	$0.615426\pi$
$110$	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	−0.720505	−	0.693450i	$-0.756090\pi$
$113$	−8.78797	+	3.19856i	−0.826703	+	0.300895i	−0.106198	+	0.994345i	$0.533868\pi$
$114$		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	−0.989379	−	0.145362i	$-0.953565\pi$
$131$	−0.113884	+	0.645866i	−0.00995006	+	0.0564296i	0.979428	+	0.201792i	$0.0646764\pi$
$132$		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	−0.316955	−	0.948441i	$-0.602660\pi$
$137$	6.57849	−	5.52001i	0.562038	−	0.471606i	0.878993	+	0.476835i	$0.158216\pi$
$138$		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	0.892681	−	0.450690i	$-0.148822\pi$
$149$	7.37093	+	6.18495i	0.603850	+	0.506691i	−0.288830	+	0.957380i	$0.593266\pi$
$150$		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	−0.627397	−	0.778700i	$-0.715880\pi$
$167$	−7.85026	+	2.85726i	−0.607472	+	0.221102i	0.0199249	+	0.999801i	$0.493657\pi$
$168$		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	−0.589834	−	0.807525i	$-0.700807\pi$
$173$	−20.5283	−	7.47170i	−1.56074	−	0.568063i	−0.970906	+	0.239462i	$0.923029\pi$
$174$		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	−0.644709	−	0.764428i	$-0.723022\pi$
$179$	4.54433	−	7.87101i	0.339659	−	0.588307i	0.984369	+	0.176121i	$0.0563549\pi$
$180$		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	−0.248203	−	0.968708i	$-0.579840\pi$
$191$	9.15854	−	7.68493i	0.662689	−	0.556062i	0.910891	+	0.412646i	$0.135395\pi$
$192$		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	0.703641	−	0.710556i	$-0.251557\pi$
$197$	−3.69895	−	6.40677i	−0.263539	−	0.456464i	−0.967180	+	0.254093i	$0.918223\pi$
$198$		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	0.647597	−	0.761983i	$-0.275774\pi$
$227$	9.85186	+	3.58578i	0.653891	+	0.237997i	0.00629435	+	0.999980i	$0.497996\pi$
$228$		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	−0.963230	−	0.268676i	$-0.913414\pi$
$233$	−3.79982	+	6.58149i	−0.248935	+	0.431167i	0.714296	+	0.699844i	$0.246747\pi$
$234$		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	$-0.764550\pi$
$239$	2.87539	−	16.3071i	0.185993	−	1.05482i	0.924673	−	0.380763i	$-0.124339\pi$
$240$		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	0.687099	−	0.726563i	$-0.258884\pi$
$251$	−4.52591	−	7.83910i	−0.285673	−	0.494800i	−0.972772	+	0.231764i	$0.925550\pi$
$252$		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	0.844418	−	0.535684i	$-0.179946\pi$
$257$	7.43054	+	6.23496i	0.463504	+	0.388926i	−0.380914	+	0.924610i	$0.624391\pi$
$258$		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	$-0.745044\pi$
$263$	−4.66336	−	26.4473i	−0.287555	−	1.63081i	0.408457	−	0.912778i	$-0.366067\pi$
$264$		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	$-0.383505\pi$
$269$	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	$0.498602\pi$
$272$	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	0.966817	−	0.255470i	$-0.0822302\pi$
$281$	25.8692	+	9.41563i	1.54323	+	0.561689i	0.576412	+	0.817159i	$0.304452\pi$
$282$		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	$-0.760980\pi$
$293$	3.23980	−	18.3738i	0.189271	−	1.07341i	0.920344	−	0.391110i	$-0.127909\pi$
$294$		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	$0.164226\pi$
$311$	26.5715	+	22.2961i	1.50673	+	1.26430i	0.636896	+	0.770950i	$0.280218\pi$
$312$		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	$0.281289\pi$
$317$	5.38879	+	30.5613i	0.302665	+	1.71650i	−0.331634	+	0.943408i	$0.607600\pi$
$318$		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	$-0.868608\pi$
$347$	1.52679	−	8.65883i	0.0819622	−	0.464831i	0.997971	−	0.0636721i	$-0.0202812\pi$
$348$		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	$0.622625\pi$
$353$	−25.4330	+	21.3409i	−1.35366	+	1.13586i	−0.977883	+	0.209150i	$0.932930\pi$
$354$		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	0.923868	−	0.382710i	$-0.125009\pi$
$359$	2.47257	+	4.28262i	0.130497	+	0.226028i	−0.793371	+	0.608738i	$0.791676\pi$
$360$		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	−0.343092	−	0.939302i	$-0.611474\pi$
$383$	−0.0419788	+	0.0152790i	−0.00214502	+	0.000780722i	0.340947	+	0.940082i	$0.389252\pi$
$384$		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	0.789463	−	0.613798i	$-0.210359\pi$
$389$	19.7169	+	7.17636i	0.999685	+	0.363856i	0.210222	+	0.977654i	$0.432581\pi$
$390$		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	$0.272755\pi$
$401$	−4.38571	+	24.8726i	−0.219012	+	1.24208i	−0.873807	+	0.486273i	$0.838356\pi$
$402$		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	−0.170931	−	0.985283i	$-0.554677\pi$
$419$	−23.9683	−	20.1118i	−1.17093	−	0.982524i	−0.999996	+	0.00275857i	$0.999122\pi$
$420$		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	$-0.596732\pi$
$431$	−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	$0.505818\pi$
$434$	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	0.0185388	−	0.999828i	$-0.494099\pi$
$443$	−12.8377	−	4.67254i	−0.609937	−	0.221999i	−0.628476	+	0.777829i	$0.716321\pi$
$444$		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	$-0.659602\pi$
$449$	10.9995	−	19.0516i	0.519097	−	0.899102i	0.999754	−	0.0221934i	$-0.00706496\pi$
$450$		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	−0.760803	−	0.648983i	$-0.775195\pi$
$461$	−5.44913	+	4.57236i	−0.253791	+	0.212956i	0.507011	+	0.861939i	$0.330750\pi$
$462$		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	$-0.959806\pi$
$467$	−13.0760	−	22.6482i	−0.605084	−	1.04804i	0.386955	−	0.922099i	$-0.373527\pi$
$468$		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	$-0.979148\pi$
$479$	−1.80708	−	10.2485i	−0.0825675	−	0.468264i	0.915288	−	0.402801i	$-0.131963\pi$
$480$		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	0.0439731	−	0.999033i	$-0.485998\pi$
$491$	15.9502	−	5.80541i	0.719824	−	0.261995i	0.675851	+	0.737038i	$0.263776\pi$
$492$		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	$0.518986\pi$
$503$	−20.0569	+	34.7395i	−0.894291	+	1.54896i	−0.834679	+	0.550736i	$0.814347\pi$
$504$		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	−0.959824	−	0.280604i	$-0.909465\pi$
$509$	0.859301	−	4.87334i	0.0380879	−	0.216007i	0.997911	+	0.0645972i	$0.0205763\pi$
$510$		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	0.768719	−	0.639586i	$-0.220894\pi$
$521$	−3.86979	−	6.70267i	−0.169539	−	0.293649i	−0.938258	+	0.345937i	$0.887561\pi$
$522$		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	$-0.547256\pi$
$557$	18.4687	−	31.9887i	0.782542	−	1.35540i	0.930456	−	0.366403i	$-0.119411\pi$
$558$		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	$-0.785105\pi$
$563$	3.95491	−	22.4294i	0.166680	−	0.945287i	0.947316	−	0.320301i	$-0.103784\pi$
$564$		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	0.00556781	−	0.999984i	$-0.498228\pi$
$569$	23.6468	−	19.8421i	0.991327	−	0.831822i	0.985759	+	0.168162i	$0.0537833\pi$
$570$		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	$0.0199551\pi$
$587$	1.97741	+	11.2144i	0.0816164	+	0.462870i	−0.916419	+	0.400220i	$0.868934\pi$
$588$		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	$-0.782120\pi$
$593$	−37.7324			−1.54948			−0.774742	+	0.632277i	$0.782120\pi$
$594$		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	$0.807516\pi$
$599$	−44.5021	+	16.1975i	−1.81831	+	0.661810i	−0.995639	+	0.0932901i	$0.970262\pi$
$600$		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	$0.181310\pi$
$617$	−3.32017	+	18.8296i	−0.133665	+	0.758052i	−0.975780	+	0.218754i	$0.929801\pi$
$618$		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	0.993069	−	0.117531i	$-0.0374979\pi$
$641$	0.498549	+	2.82741i	0.0196915	+	0.111676i	−0.973378	+	0.229207i	$0.926387\pi$
$642$		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	$-0.751136\pi$
$647$	−36.1004			−1.41925			−0.709626	+	0.704579i	$0.751136\pi$
$648$		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	−0.979861	−	0.199681i	$-0.936010\pi$
$653$	−40.9405	+	14.9011i	−1.60213	+	0.583126i	−0.622265	+	0.782807i	$0.713787\pi$
$654$		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	0.763294	−	0.646051i	$-0.223581\pi$
$659$	23.9443	+	8.71501i	0.932737	+	0.339489i	0.169443	+	0.985540i	$0.445803\pi$
$660$		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	$0.564425\pi$
$677$	−31.2395	+	26.2130i	−1.20063	+	1.00745i	−0.999612	+	0.0278613i	$0.991130\pi$
$678$		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	$0.0403139\pi$
$683$	15.8213	+	27.4033i	0.605384	+	1.04856i	−0.386606	+	0.922245i	$0.626353\pi$
$684$		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	$-0.454583\pi$
$701$	7.52982			0.284397			0.142199	+	0.989838i	$0.454583\pi$
$702$		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	$-0.665511\pi$
$719$	13.4913	−	23.3676i	0.503140	−	0.871464i	0.999993	−	0.00362928i	$-0.00115524\pi$
$720$		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	$-0.988020\pi$
$743$	−32.9788	−	27.6725i	−1.20987	−	1.01520i	−0.210582	−	0.977576i	$-0.567536\pi$
$744$		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	−0.506623	−	0.862168i	$-0.669106\pi$
$761$	−9.39386	+	3.41909i	−0.340527	+	0.123942i	0.166095	+	0.986110i	$0.446884\pi$
$762$		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	−0.987421	−	0.158112i	$-0.949459\pi$
$773$	−9.91954	+	17.1812i	−0.356781	+	0.617963i	0.630640	+	0.776076i	$0.282793\pi$
$774$		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

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

L-functions

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