LMFDB - Embedded newform 729.2.e.s.82.2

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			82.2
Root			$0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.s.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0300370	+	0.170348i	0.0212393	+	0.120454i	0.993584	−	0.113096i	$-0.0360768\pi$
$2$	0.0300370	+	0.170348i	0.0212393	+	0.120454i	−0.972345	+	0.233550i	$0.924966\pi$
$3$		0			0
$3$		0			0
$4$	1.85127	−	0.673807i	0.925635	−	0.336903i
$5$	−2.86237	−	2.40182i	−1.28009	−	1.07412i	−0.993231	−	0.116153i	$-0.962944\pi$
$5$	−2.86237	−	2.40182i	−1.28009	−	1.07412i	−0.286861	−	0.957972i	$-0.592612\pi$
$6$		0			0
$7$	−2.84868	−	1.03683i	−1.07670	−	0.391886i	−0.258021	−	0.966139i	$-0.583070\pi$
$7$	−2.84868	−	1.03683i	−1.07670	−	0.391886i	−0.818678	+	0.574253i	$0.805292\pi$
$8$	0.343364	+	0.594724i	0.121398	+	0.210267i
$9$		0			0
$10$	0.323168	−	0.559743i	0.102195	−	0.177006i
$11$	−1.90875	+	1.60163i	−0.575510	+	0.482910i	−0.883469	−	0.468490i	$-0.844798\pi$
$11$	−1.90875	+	1.60163i	−0.575510	+	0.482910i	0.307959	+	0.951400i	$0.400354\pi$
$12$		0			0
$13$	−0.132865	+	0.753515i	−0.0368501	+	0.208987i	−0.997673	−	0.0681742i	$-0.978283\pi$
$13$	−0.132865	+	0.753515i	−0.0368501	+	0.208987i	0.960823	+	0.277162i	$0.0893937\pi$
$14$	0.0910570	−	0.516410i	0.0243360	−	0.138016i
$15$		0			0
$16$	2.92734	−	2.45633i	0.731835	−	0.614083i
$17$	−2.31139	+	4.00345i	−0.560595	+	0.970979i	0.436850	+	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	$0.810975\pi$
$20$	−6.91738	−	2.51772i	−1.54677	−	0.562980i
$21$		0			0
$22$	−0.330168	−	0.277044i	−0.0703920	−	0.0590659i
$23$	−6.13091	+	2.23147i	−1.27838	+	0.465293i	−0.889897	−	0.456161i	$-0.849224\pi$
$23$	−6.13091	+	2.23147i	−1.27838	+	0.465293i	−0.388486	+	0.921455i	$0.627002\pi$
$24$		0			0
$25$	1.55622	+	8.82575i	0.311244	+	1.76515i
$26$	−0.132351			−0.0259561
$27$		0			0
$28$	−5.97229			−1.12866
$29$	−1.13755	−	6.45137i	−0.211238	−	1.19799i	−0.887317	−	0.461160i	$-0.847433\pi$
$29$	−1.13755	−	6.45137i	−0.211238	−	1.19799i	0.676079	−	0.736829i	$-0.263678\pi$
$30$		0			0
$31$	−6.15539	+	2.24038i	−1.10554	+	0.402384i	−0.829356	−	0.558721i	$-0.811292\pi$
$31$	−6.15539	+	2.24038i	−1.10554	+	0.402384i	−0.276184	+	0.961105i	$0.589070\pi$
$32$	1.55849	+	1.30773i	0.275504	+	0.231176i
$33$		0			0
$34$	−0.751407	−	0.273490i	−0.128865	−	0.0469031i
$35$	5.66369	+	9.80980i	0.957338	+	1.65816i
$36$		0			0
$37$	−2.47984	+	4.29522i	−0.407684	+	0.706129i	−0.994630	−	0.103497i	$-0.966997\pi$
$37$	−2.47984	+	4.29522i	−0.407684	+	0.706129i	0.586946	+	0.809626i	$0.300330\pi$
$38$	−0.0810738	+	0.0680290i	−0.0131519	+	0.0110358i
$39$		0			0
$40$	0.445582	−	2.52702i	0.0704527	−	0.399557i
$41$	0.913431	−	5.18032i	0.142654	−	0.809031i	−0.826567	−	0.562838i	$-0.809709\pi$
$41$	0.913431	−	5.18032i	0.142654	−	0.809031i	0.969221	−	0.246192i	$-0.0791795\pi$
$42$		0			0
$43$	4.26731	−	3.58070i	0.650758	−	0.546051i	−0.256543	−	0.966533i	$-0.582583\pi$
$43$	4.26731	−	3.58070i	0.650758	−	0.546051i	0.907301	+	0.420482i	$0.138139\pi$
$44$	−2.45442	+	4.25118i	−0.370018	+	0.640889i
$45$		0			0
$46$	−0.564280	−	0.977362i	−0.0831986	−	0.144104i
$47$	−1.04082	−	0.378827i	−0.151819	−	0.0552576i	0.264993	−	0.964250i	$-0.414630\pi$
$47$	−1.04082	−	0.378827i	−0.151819	−	0.0552576i	−0.416812	+	0.908993i	$0.636853\pi$
$48$		0			0
$49$	1.67762	+	1.40769i	0.239660	+	0.201099i
$50$	−1.45670	+	0.530197i	−0.206009	+	0.0749812i
$51$		0			0
$52$	0.261754	+	1.48448i	0.0362988	+	0.205861i
$53$	8.84310			1.21469			0.607346	−	0.794437i	$-0.292234\pi$
$53$	8.84310			1.21469			0.607346	+	0.794437i	$0.292234\pi$
$54$		0			0
$55$	9.31038			1.25541
$56$	−0.361503	−	2.05019i	−0.0483079	−	0.273968i
$57$		0			0
$58$	1.06481	−	0.387559i	0.139816	−	0.0508890i
$59$	−9.07897	−	7.61816i	−1.18198	−	0.991800i	−0.999964	−	0.00850504i	$-0.997293\pi$
$59$	−9.07897	−	7.61816i	−1.18198	−	0.991800i	−0.182018	−	0.983295i	$-0.558263\pi$
$60$		0			0
$61$	−7.69327	−	2.80012i	−0.985022	−	0.358519i	−0.201231	−	0.979544i	$-0.564494\pi$
$61$	−7.69327	−	2.80012i	−0.985022	−	0.358519i	−0.783791	+	0.621025i	$0.786716\pi$
$62$	−0.566533	−	0.981264i	−0.0719498	−	0.124621i
$63$		0			0
$64$	3.64541	−	6.31404i	0.455677	−	0.789255i
$65$	2.19011	−	1.83772i	0.271650	−	0.227941i
$66$		0			0
$67$	−0.210520	+	1.19392i	−0.0257192	+	0.145861i	−0.994963	−	0.100241i	$-0.968039\pi$
$67$	−0.210520	+	1.19392i	−0.0257192	+	0.145861i	0.969244	+	0.246102i	$0.0791497\pi$
$68$	−1.58146	+	8.96889i	−0.191780	+	1.08764i
$69$		0			0
$70$	−1.50096	+	1.25946i	−0.179399	+	0.150534i
$71$	2.45973	−	4.26038i	0.291916	−	0.505614i	−0.682346	−	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	$0.914292\pi$
$74$	−0.806169	−	0.293421i	−0.0937152	−	0.0341095i
$75$		0			0
$76$	0.923375	+	0.774804i	0.105918	+	0.0888761i
$77$	7.09803	−	2.58347i	0.808896	−	0.294414i
$78$		0			0
$79$	−2.04811	−	11.6154i	−0.230431	−	1.30684i	−0.852027	−	0.523499i	$-0.824627\pi$
$79$	−2.04811	−	11.6154i	−0.230431	−	1.30684i	0.621596	−	0.783338i	$-0.286485\pi$
$80$	−14.2788			−1.59642
$81$		0			0
$82$	0.909895			0.100481
$83$	1.56562	+	8.87910i	0.171850	+	0.974608i	0.941718	+	0.336404i	$0.109211\pi$
$83$	1.56562	+	8.87910i	0.171850	+	0.974608i	−0.769868	+	0.638203i	$0.779678\pi$
$84$		0			0
$85$	16.2316	−	5.90782i	1.76057	−	0.640793i
$86$	0.738141	+	0.619374i	0.0795958	+	0.0667888i
$87$		0			0
$88$	−1.60792	−	0.585237i	−0.171405	−	0.0623865i
$89$	−3.76943	−	6.52884i	−0.399558	−	0.692055i	0.594113	−	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
$92$	−9.84638	+	8.26210i	−1.02656	+	0.861383i
$93$		0			0
$94$	0.0332694	−	0.188680i	0.00343148	−	0.0194609i
$95$	0.396993	−	2.25146i	0.0407306	−	0.230995i
$96$		0			0
$97$	−0.726481	+	0.609590i	−0.0737630	+	0.0618945i	−0.678924	−	0.734209i	$-0.737553\pi$
$97$	−0.726481	+	0.609590i	−0.0737630	+	0.0618945i	0.605161	+	0.796103i	$0.293109\pi$
$98$	−0.189407	+	0.328062i	−0.0191330	+	0.0331393i
$99$		0			0
$100$	8.82783	+	15.2902i	0.882783	+	1.52902i
$101$	5.26994	+	1.91810i	0.524379	+	0.190858i	0.590627	−	0.806945i	$-0.298881\pi$
$101$	5.26994	+	1.91810i	0.524379	+	0.190858i	−0.0662479	+	0.997803i	$0.521103\pi$
$102$		0			0
$103$	−7.21998	−	6.05829i	−0.711406	−	0.596941i	0.213587	−	0.976924i	$-0.431485\pi$
$103$	−7.21998	−	6.05829i	−0.711406	−	0.596941i	−0.924993	+	0.379983i	$0.875930\pi$
$104$	−0.493754	+	0.179712i	−0.0484166	+	0.0176222i
$105$		0			0
$106$	0.265620	+	1.50640i	0.0257993	+	0.146315i
$107$	−1.27825			−0.123573			−0.0617864	−	0.998089i	$-0.519680\pi$
$107$	−1.27825			−0.123573			−0.0617864	+	0.998089i	$0.519680\pi$
$108$		0			0
$109$	−7.40689			−0.709451			−0.354726	−	0.934970i	$-0.615426\pi$
$109$	−7.40689			−0.709451			−0.354726	+	0.934970i	$0.615426\pi$
$110$	0.279655	+	1.58600i	0.0266641	+	0.151220i
$111$		0			0
$112$	−10.8858	+	3.96212i	−1.02862	+	0.374386i
$113$	7.16402	+	6.01133i	0.673934	+	0.565498i	0.914227	−	0.405203i	$-0.132799\pi$
$113$	7.16402	+	6.01133i	0.673934	+	0.565498i	−0.240293	+	0.970700i	$0.577243\pi$
$114$		0			0
$115$	22.9085	+	8.33802i	2.13623	+	0.777524i
$116$	−6.45289	−	11.1767i	−0.599136	−	1.03773i
$117$		0			0
$118$	1.02503	−	1.77541i	0.0943621	−	0.163440i
$119$	10.7353	−	9.00800i	0.984105	−	0.825762i
$120$		0			0
$121$	−0.832027	+	4.71866i	−0.0756388	+	0.428969i
$122$	0.245913	−	1.39464i	0.0222639	−	0.126265i
$123$		0			0
$124$	−9.88569	+	8.29508i	−0.887762	+	0.744920i
$125$	7.40194	−	12.8205i	0.662050	−	1.14670i
$126$		0			0
$127$	−10.3984	−	18.0106i	−0.922710	−	1.59818i	−0.795204	−	0.606342i	$-0.792636\pi$
$127$	−10.3984	−	18.0106i	−0.922710	−	1.59818i	−0.127505	−	0.991838i	$-0.540697\pi$
$128$	5.00862	+	1.82299i	0.442704	+	0.161131i
$129$		0			0
$130$	0.378837	+	0.317882i	0.0332262	+	0.0278801i
$131$	0.616278	−	0.224307i	0.0538445	−	0.0195978i	−0.314958	−	0.949106i	$-0.601990\pi$
$131$	0.616278	−	0.224307i	0.0538445	−	0.0195978i	0.368802	+	0.929508i	$0.379768\pi$
$132$		0			0
$133$	−0.322083	−	1.82662i	−0.0279282	−	0.158388i
$134$	−0.209705			−0.0181158
$135$		0			0
$136$	−3.17460			−0.272219
$137$	1.49122	+	8.45714i	0.127404	+	0.722542i	0.979851	+	0.199729i	$0.0640063\pi$
$137$	1.49122	+	8.45714i	0.127404	+	0.722542i	−0.852447	+	0.522813i	$0.824883\pi$
$138$		0			0
$139$	−12.6352	+	4.59885i	−1.07171	+	0.390069i	−0.816815	−	0.576900i	$-0.804262\pi$
$139$	−12.6352	+	4.59885i	−1.07171	+	0.390069i	−0.254892	+	0.966969i	$0.582040\pi$
$140$	17.0949	+	14.3443i	1.44478	+	1.21232i
$141$		0			0
$142$	0.799630	+	0.291042i	0.0671035	+	0.0244237i
$143$	−0.953247	−	1.65107i	−0.0797145	−	0.138070i
$144$		0			0
$145$	−12.2389	+	21.1984i	−1.01639	+	1.76043i
$146$	0.569708	−	0.478042i	0.0471494	−	0.0395630i
$147$		0			0
$148$	−1.69671	+	9.62254i	−0.139469	+	0.790968i
$149$	1.67085	−	9.47589i	0.136882	−	0.776295i	−0.836649	−	0.547739i	$-0.815489\pi$
$149$	1.67085	−	9.47589i	0.136882	−	0.776295i	0.973531	−	0.228556i	$-0.0734003\pi$
$150$		0			0
$151$	−5.46052	+	4.58192i	−0.444371	+	0.372871i	−0.837342	−	0.546679i	$-0.815892\pi$
$151$	−5.46052	+	4.58192i	−0.444371	+	0.372871i	0.392971	+	0.919551i	$0.371447\pi$
$152$	−0.210085	+	0.363878i	−0.0170402	+	0.0295144i
$153$		0			0
$154$	0.653293	+	1.13154i	0.0526439	+	0.0911818i
$155$	23.0000	+	8.37131i	1.84740	+	0.672400i
$156$		0			0
$157$	5.88764	+	4.94032i	0.469885	+	0.394280i	0.846753	−	0.531987i	$-0.178554\pi$
$157$	5.88764	+	4.94032i	0.469885	+	0.394280i	−0.376868	+	0.926267i	$0.622999\pi$
$158$	1.91714	−	0.697784i	0.152520	−	0.0555127i
$159$		0			0
$160$	−1.32005	−	7.48640i	−0.104360	−	0.591852i
$161$	19.7786			1.55877
$162$		0			0
$163$	1.04750			0.0820465			0.0410232	−	0.999158i	$-0.486938\pi$
$163$	1.04750			0.0820465			0.0410232	+	0.999158i	$0.486938\pi$
$164$	−1.79953	−	10.2056i	−0.140520	−	0.796927i
$165$		0			0
$166$	−1.46551	+	0.533402i	−0.113746	+	0.0414000i
$167$	6.39959	+	5.36990i	0.495215	+	0.415535i	0.855891	−	0.517156i	$-0.173009\pi$
$167$	6.39959	+	5.36990i	0.495215	+	0.415535i	−0.360676	+	0.932691i	$0.617454\pi$
$168$		0			0
$169$	11.6659	+	4.24603i	0.897375	+	0.326618i
$170$	1.49393	+	2.58757i	0.114580	+	0.198458i
$171$		0			0
$172$	5.48724	−	9.50417i	0.418398	−	0.724686i
$173$	16.7348	−	14.0422i	1.27233	−	1.06761i	0.278073	−	0.960560i	$-0.410304\pi$
$173$	16.7348	−	14.0422i	1.27233	−	1.06761i	0.994254	−	0.107049i	$-0.0341402\pi$
$174$		0			0
$175$	4.71767	−	26.7552i	0.356622	−	2.02251i
$176$	−1.65343	+	9.37704i	−0.124632	+	0.706821i
$177$		0			0
$178$	0.998953	−	0.838221i	0.0748747	−	0.0628273i
$179$	4.54433	−	7.87101i	0.339659	−	0.588307i	−0.644709	−	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	$0.747957\pi$
$182$	0.377024	+	0.137225i	0.0279469	+	0.0101718i
$183$		0			0
$184$	−3.43224	−	2.87999i	−0.253028	−	0.212316i
$185$	17.4146	−	6.33838i	1.28034	−	0.466007i
$186$		0			0
$187$	−2.00018	−	11.3436i	−0.146268	−	0.829525i
$188$	−2.18209			−0.159145
$189$		0			0
$190$	0.395456			0.0286894
$191$	2.07607	+	11.7740i	0.150219	+	0.851936i	0.963027	+	0.269404i	$0.0868268\pi$
$191$	2.07607	+	11.7740i	0.150219	+	0.851936i	−0.812808	+	0.582532i	$0.802062\pi$
$192$		0			0
$193$	8.33849	−	3.03496i	0.600218	−	0.218461i	−0.0239999	−	0.999712i	$-0.507640\pi$
$193$	8.33849	−	3.03496i	0.600218	−	0.218461i	0.624218	+	0.781251i	$0.285418\pi$
$194$	−0.125664	−	0.105444i	−0.00902214	−	0.00757047i
$195$		0			0
$196$	4.05424	+	1.47562i	0.289589	+	0.105402i
$197$	−3.69895	−	6.40677i	−0.263539	−	0.456464i	0.703641	−	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	$0.0466948\pi$
$200$	−4.71454	+	3.95597i	−0.333368	+	0.279729i
$201$		0			0
$202$	−0.168452	+	0.955338i	−0.0118522	+	0.0672174i
$203$	−3.44848	+	19.5573i	−0.242036	+	1.37265i
$204$		0			0
$205$	−15.0568	+	12.6341i	−1.05161	+	0.882406i
$206$	0.815151	−	1.41188i	0.0567942	−	0.0983705i
$207$		0			0
$208$	1.46194	+	2.53215i	0.101367	+	0.175573i
$209$	−1.43259	−	0.521420i	−0.0990942	−	0.0360674i
$210$		0			0
$211$	15.9806	+	13.4093i	1.10015	+	0.923133i	0.997435	−	0.0715777i	$-0.0228034\pi$
$211$	15.9806	+	13.4093i	1.10015	+	0.923133i	0.102712	+	0.994711i	$0.467248\pi$
$212$	16.3710	−	5.95854i	1.12436	−	0.409234i
$213$		0			0
$214$	−0.0383946	−	0.217747i	−0.00262460	−	0.0148849i
$215$	−20.8148			−1.41956
$216$		0			0
$217$	19.8576			1.34802
$218$	−0.222480	−	1.26175i	−0.0150683	−	0.0854564i
$219$		0			0
$220$	17.2360	−	6.27340i	1.16205	−	0.422952i
$221$	−2.70955	−	2.27358i	−0.182264	−	0.152938i
$222$		0			0
$223$	−22.1565	−	8.06432i	−1.48371	−	0.540027i	−0.531926	−	0.846791i	$-0.678531\pi$
$223$	−22.1565	−	8.06432i	−1.48371	−	0.540027i	−0.951786	+	0.306764i	$0.900754\pi$
$224$	−3.08373	−	5.34118i	−0.206041	−	0.356873i
$225$		0			0
$226$	−0.808832	+	1.40094i	−0.0538027	+	0.0931890i
$227$	−8.03131	+	6.73907i	−0.533057	+	0.447288i	−0.869155	−	0.494539i	$-0.835337\pi$
$227$	−8.03131	+	6.73907i	−0.533057	+	0.447288i	0.336099	+	0.941827i	$0.390892\pi$
$228$		0			0
$229$	−2.41066	+	13.6715i	−0.159301	+	0.903439i	0.795447	+	0.606023i	$0.207236\pi$
$229$	−2.41066	+	13.6715i	−0.159301	+	0.903439i	−0.954748	+	0.297416i	$0.903875\pi$
$230$	−0.732263	+	4.15287i	−0.0482840	+	0.273832i
$231$		0			0
$232$	3.44619	−	2.89170i	0.226254	−	0.189849i
$233$	−3.79982	+	6.58149i	−0.248935	+	0.431167i	−0.963230	−	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
$236$	−21.9408	−	7.98579i	−1.42822	−	0.519831i
$237$		0			0
$238$	1.85695	+	1.55817i	0.120368	+	0.101001i
$239$	−15.5601	+	5.66340i	−1.00650	+	0.366335i	−0.792087	−	0.610408i	$-0.791005\pi$
$239$	−15.5601	+	5.66340i	−1.00650	+	0.366335i	−0.214411	+	0.976744i	$0.568783\pi$
$240$		0			0
$241$	−2.52111	−	14.2979i	−0.162399	−	0.921010i	−0.951706	−	0.307011i	$-0.900671\pi$
$241$	−2.52111	−	14.2979i	−0.162399	−	0.921010i	0.789307	−	0.613999i	$-0.210440\pi$
$242$	−0.828806			−0.0532776
$243$		0			0
$244$	−16.1290			−1.03256
$245$	−1.42096	−	8.05867i	−0.0907819	−	0.514850i
$246$		0			0
$247$	−0.439913	+	0.160115i	−0.0279910	+	0.0101879i
$248$	−3.44595	−	2.89149i	−0.218818	−	0.183610i
$249$		0			0
$250$	2.40629	+	0.875816i	0.152187	+	0.0553915i
$251$	−4.52591	−	7.83910i	−0.285673	−	0.494800i	0.687099	−	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
$254$	2.75573	−	2.31233i	0.172910	−	0.145089i
$255$		0			0
$256$	2.37198	−	13.4522i	0.148249	−	0.840760i
$257$	1.68437	−	9.55251i	0.105068	−	0.595870i	−0.886125	−	0.463446i	$-0.846613\pi$
$257$	1.68437	−	9.55251i	0.105068	−	0.595870i	0.991193	−	0.132424i	$-0.0422760\pi$
$258$		0			0
$259$	11.5177	−	9.66449i	0.715675	−	0.600522i
$260$	2.81622	−	4.87783i	0.174654	−	0.302510i
$261$		0			0
$262$	0.0567214	+	0.0982443i	0.00350426	+	0.00606955i
$263$	25.2357	+	9.18503i	1.55610	+	0.566373i	0.969838	−	0.243749i	$-0.0783775\pi$
$263$	25.2357	+	9.18503i	1.55610	+	0.566373i	0.586260	+	0.810123i	$0.300600\pi$
$264$		0			0
$265$	−25.3122	−	21.2395i	−1.55492	−	1.30473i
$266$	0.301488	−	0.109732i	0.0184854	−	0.00672813i
$267$		0			0
$268$	0.414742	+	2.35212i	0.0253344	+	0.143678i
$269$	11.7388			0.715729			0.357865	−	0.933774i	$-0.383505\pi$
$269$	11.7388			0.715729			0.357865	+	0.933774i	$0.383505\pi$
$270$		0			0
$271$	0.144576			0.00878238			0.00439119	−	0.999990i	$-0.498602\pi$
$271$	0.144576			0.00878238			0.00439119	+	0.999990i	$0.498602\pi$
$272$	3.06756	+	17.3970i	0.185998	+	1.05485i
$273$		0			0
$274$	−1.39587	+	0.508053i	−0.0843273	+	0.0306926i
$275$	−17.1060	−	14.3537i	−1.03153	−	0.865558i
$276$		0			0
$277$	0.953248	+	0.346954i	0.0572751	+	0.0208464i	0.370499	−	0.928833i	$-0.379187\pi$
$277$	0.953248	+	0.346954i	0.0572751	+	0.0208464i	−0.313224	+	0.949679i	$0.601409\pi$
$278$	−1.16293	−	2.01425i	−0.0697479	−	0.120807i
$279$		0			0
$280$	−3.88942	+	6.73667i	−0.232437	+	0.402593i
$281$	−21.0888	+	17.6956i	−1.25805	+	1.05563i	−0.262165	+	0.965023i	$0.584436\pi$
$281$	−21.0888	+	17.6956i	−1.25805	+	1.05563i	−0.995887	+	0.0906075i	$0.971119\pi$
$282$		0			0
$283$	−4.65427	+	26.3957i	−0.276668	+	1.56906i	0.456946	+	0.889494i	$0.348943\pi$
$283$	−4.65427	+	26.3957i	−0.276668	+	1.56906i	−0.733614	+	0.679566i	$0.762168\pi$
$284$	1.68295	−	9.54449i	0.0998648	−	0.566361i
$285$		0			0
$286$	0.252624	−	0.211977i	0.0149380	−	0.0125345i
$287$	−7.97320	+	13.8100i	−0.470643	+	0.815178i
$288$		0			0
$289$	−2.18506	−	3.78464i	−0.128533	−	0.222626i
$290$	−3.97873	−	1.44814i	−0.233639	−	0.0850376i
$291$		0			0
$292$	−6.48859	−	5.44458i	−0.379716	−	0.318620i
$293$	−17.5321	+	6.38116i	−1.02424	+	0.372791i	−0.798883	−	0.601486i	$-0.794576\pi$
$293$	−17.5321	+	6.38116i	−1.02424	+	0.372791i	−0.225352	+	0.974277i	$0.572353\pi$
$294$		0			0
$295$	7.68998	+	43.6120i	0.447728	+	2.53919i
$296$	−3.40596			−0.197967
$297$		0			0
$298$	1.66439			0.0964153
$299$	−0.866861	−	4.91621i	−0.0501319	−	0.284312i
$300$		0			0
$301$	−15.8688	+	5.77576i	−0.914660	+	0.332909i
$302$	−0.944539	−	0.792562i	−0.0543521	−	0.0456068i
$303$		0			0
$304$	2.19708	+	0.799671i	0.126011	+	0.0458643i
$305$	15.2956	+	26.4928i	0.875825	+	1.51697i
$306$		0			0
$307$	−16.8946	+	29.2624i	−0.964227	+	1.67009i	−0.252551	+	0.967584i	$0.581269\pi$
$307$	−16.8946	+	29.2624i	−0.964227	+	1.67009i	−0.711677	+	0.702507i	$0.752064\pi$
$308$	11.3996	−	9.56541i	0.649553	−	0.545040i
$309$		0			0
$310$	−0.735187	+	4.16945i	−0.0417558	+	0.236809i
$311$	6.02326	−	34.1596i	0.341548	−	1.93701i	−0.00766664	−	0.999971i	$-0.502440\pi$
$311$	6.02326	−	34.1596i	0.341548	−	1.93701i	0.349214	−	0.937043i	$-0.386448\pi$
$312$		0			0
$313$	2.55888	−	2.14716i	0.144636	−	0.121364i	−0.567599	−	0.823305i	$-0.692127\pi$
$313$	2.55888	−	2.14716i	0.144636	−	0.121364i	0.712235	+	0.701941i	$0.247683\pi$
$314$	−0.664726	+	1.15134i	−0.0375127	+	0.0649739i
$315$		0			0
$316$	−11.6182	−	20.1232i	−0.653572	−	1.13202i
$317$	−29.1613	−	10.6138i	−1.63786	−	0.596133i	−0.651198	−	0.758908i	$-0.725733\pi$
$317$	−29.1613	−	10.6138i	−1.63786	−	0.596133i	−0.986663	+	0.162775i	$0.947956\pi$
$318$		0			0
$319$	12.5040	+	10.4921i	0.700090	+	0.587446i
$320$	−25.5997	+	9.31753i	−1.43107	+	0.520866i
$321$		0			0
$322$	0.594090	+	3.36925i	0.0331073	+	0.187761i
$323$	−2.82842			−0.157378
$324$		0			0
$325$	−6.85710			−0.380363
$326$	0.0314637	+	0.178440i	0.00174261	+	0.00988285i
$327$		0			0
$328$	3.39450	−	1.23550i	0.187430	−	0.0682190i
$329$	2.57217	+	2.15831i	0.141809	+	0.118992i
$330$		0			0
$331$	−3.07437	−	1.11898i	−0.168983	−	0.0615047i	0.256143	−	0.966639i	$-0.417548\pi$
$331$	−3.07437	−	1.11898i	−0.168983	−	0.0615047i	−0.425126	+	0.905134i	$0.639770\pi$
$332$	8.88119	+	15.3827i	0.487419	+	0.844234i
$333$		0			0
$334$	−0.722527	+	1.25145i	−0.0395349	+	0.0684765i
$335$	3.47016	−	2.91181i	0.189595	−	0.159089i
$336$		0			0
$337$	1.10541	−	6.26910i	0.0602156	−	0.341500i	−0.939784	−	0.341768i	$-0.888974\pi$
$337$	1.10541	−	6.26910i	0.0602156	−	0.341500i	1.00000		0.000268386i	$8.54299e-5\pi$
$338$	−0.372896	+	2.11480i	−0.0202829	+	0.115030i
$339$		0			0
$340$	26.0683	−	21.8739i	1.41375	−	1.18628i
$341$	8.16083	−	14.1350i	0.441934	−	0.765452i
$342$		0			0
$343$	7.29078	+	12.6280i	0.393665	+	0.681848i
$344$	3.59477	+	1.30839i	0.193817	+	0.0705435i
$345$		0			0
$346$	2.89473	+	2.42896i	0.155621	+	0.130582i
$347$	−8.26216	+	3.00718i	−0.443536	+	0.161434i	−0.554127	−	0.832432i	$-0.686948\pi$
$347$	−8.26216	+	3.00718i	−0.443536	+	0.161434i	0.110591	+	0.993866i	$0.464726\pi$
$348$		0			0
$349$	2.50057	+	14.1815i	0.133853	+	0.759116i	0.975652	+	0.219325i	$0.0703855\pi$
$349$	2.50057	+	14.1815i	0.133853	+	0.759116i	−0.841799	+	0.539791i	$0.818503\pi$
$350$	4.69941			0.251194
$351$		0			0
$352$	−5.06926			−0.270192
$353$	−5.76520	−	32.6961i	−0.306851	−	1.74024i	−0.614663	−	0.788790i	$-0.710708\pi$
$353$	−5.76520	−	32.6961i	−0.306851	−	1.74024i	0.307812	−	0.951447i	$-0.400403\pi$
$354$		0			0
$355$	−17.2733	+	6.28697i	−0.916773	+	0.333678i
$356$	−11.3774	−	9.54677i	−0.603001	−	0.505978i
$357$		0			0
$358$	1.47731	+	0.537697i	0.0780782	+	0.0284182i
$359$	2.47257	+	4.28262i	0.130497	+	0.226028i	0.923868	−	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
$362$	−0.944879	+	0.792848i	−0.0496617	+	0.0416711i
$363$		0			0
$364$	0.793508	−	4.50021i	0.0415911	−	0.235875i
$365$	−2.78969	+	15.8211i	−0.146019	+	0.828114i
$366$		0			0
$367$	−1.90933	+	1.60212i	−0.0996662	+	0.0836299i	−0.691259	−	0.722607i	$-0.742944\pi$
$367$	−1.90933	+	1.60212i	−0.0996662	+	0.0836299i	0.591593	+	0.806237i	$0.298499\pi$
$368$	−12.4660	+	21.5918i	−0.649837	+	1.12555i
$369$		0			0
$370$	1.60281	+	2.77615i	0.0833262	+	0.144325i
$371$	−25.1911	−	9.16882i	−1.30786	−	0.476021i
$372$		0			0
$373$	−21.4857	−	18.0286i	−1.11249	−	0.933487i	−0.114286	−	0.993448i	$-0.536458\pi$
$373$	−21.4857	−	18.0286i	−1.11249	−	0.933487i	−0.998201	+	0.0599605i	$0.980903\pi$
$374$	1.87228	−	0.681453i	0.0968131	−	0.0352371i
$375$		0			0
$376$	−0.132082	−	0.749075i	−0.00681162	−	0.0386306i
$377$	5.01234			0.258149
$378$		0			0
$379$	5.13991			0.264019			0.132010	−	0.991248i	$-0.457857\pi$
$379$	5.13991			0.264019			0.132010	+	0.991248i	$0.457857\pi$
$380$	−0.782108	−	4.43556i	−0.0401213	−	0.227539i
$381$		0			0
$382$	−1.94332	+	0.707310i	−0.0994288	+	0.0361891i
$383$	0.0342214	+	0.0287152i	0.00174863	+	0.00146728i	0.643662	−	0.765310i	$-0.277414\pi$
$383$	0.0342214	+	0.0287152i	0.00174863	+	0.00146728i	−0.641913	+	0.766778i	$0.721859\pi$
$384$		0			0
$385$	−26.5223	−	9.65331i	−1.35170	−	0.491978i
$386$	0.767463	+	1.32928i	0.0390628	+	0.0676588i
$387$		0			0
$388$	−0.934167	+	1.61802i	−0.0474251	+	0.0821427i
$389$	−16.0733	+	13.4871i	−0.814951	+	0.683825i	−0.951784	−	0.306769i	$-0.900752\pi$
$389$	−16.0733	+	13.4871i	−0.814951	+	0.683825i	0.136833	+	0.990594i	$0.456308\pi$
$390$		0			0
$391$	5.23736	−	29.7026i	0.264865	−	1.50212i
$392$	−0.261153	+	1.48107i	−0.0131902	+	0.0748054i
$393$		0			0
$394$	0.980276	−	0.822549i	0.0493856	−	0.0414394i
$395$	−22.0356	+	38.1668i	−1.10873	+	1.92038i
$396$		0			0
$397$	0.00122821	+	0.00212731i	6.16419e−5	+	0.000106767i	0.866056	−	0.499947i	$-0.166647\pi$
$397$	0.00122821	+	0.00212731i	6.16419e−5	+	0.000106767i	−0.865995	+	0.500053i	$0.833314\pi$
$398$	1.68782	+	0.614316i	0.0846027	+	0.0307929i
$399$		0			0
$400$	26.2345	+	22.0134i	1.31173	+	1.10067i
$401$	23.7332	−	8.63817i	1.18518	−	0.431370i	0.327150	−	0.944972i	$-0.393912\pi$
$401$	23.7332	−	8.63817i	1.18518	−	0.431370i	0.858028	+	0.513603i	$0.171689\pi$
$402$		0			0
$403$	−0.870322	−	4.93584i	−0.0433538	−	0.245872i
$404$	11.0485			0.549684
$405$		0			0
$406$	−3.43513			−0.170483
$407$	−2.14595	−	12.1703i	−0.106371	−	0.603259i
$408$		0			0
$409$	21.8841	−	7.96515i	1.08210	−	0.393851i	0.261410	−	0.965228i	$-0.415813\pi$
$409$	21.8841	−	7.96515i	1.08210	−	0.393851i	0.820688	+	0.571377i	$0.193590\pi$
$410$	−2.60446	−	2.18540i	−0.128625	−	0.107929i
$411$		0			0
$412$	−17.4482	−	6.35064i	−0.859613	−	0.312874i
$413$	17.9643	+	31.1151i	0.883965	+	1.53107i
$414$		0			0
$415$	16.8446	−	29.1756i	0.826867	−	1.43218i
$416$	−1.19246	+	1.00059i	−0.0584651	+	0.0490581i
$417$		0			0
$418$	0.0457922	−	0.259701i	0.00223977	−	0.0127024i
$419$	−5.43317	+	30.8130i	−0.265428	+	1.50531i	0.502387	+	0.864643i	$0.332455\pi$
$419$	−5.43317	+	30.8130i	−0.265428	+	1.50531i	−0.767815	+	0.640672i	$0.778656\pi$
$420$		0			0
$421$	23.3870	−	19.6240i	1.13981	−	0.956417i	0.140381	−	0.990098i	$-0.455167\pi$
$421$	23.3870	−	19.6240i	1.13981	−	0.956417i	0.999433	+	0.0336807i	$0.0107229\pi$
$422$	−1.80424	+	3.12503i	−0.0878289	+	0.152124i
$423$		0			0
$424$	3.03640	+	5.25920i	0.147461	+	0.255409i
$425$	−38.9304	−	14.1695i	−1.88840	−	0.687323i
$426$		0			0
$427$	19.0124	+	15.9533i	0.920073	+	0.772033i
$428$	−2.36638	+	0.861291i	−0.114383	+	0.0416321i
$429$		0			0
$430$	−0.625213	−	3.54576i	−0.0301505	−	0.170992i
$431$	−12.4246			−0.598474			−0.299237	−	0.954179i	$-0.596732\pi$
$431$	−12.4246			−0.598474			−0.299237	+	0.954179i	$0.596732\pi$
$432$		0			0
$433$	−0.760649			−0.0365545			−0.0182772	−	0.999833i	$-0.505818\pi$
$433$	−0.760649			−0.0365545			−0.0182772	+	0.999833i	$0.505818\pi$
$434$	0.596462	+	3.38270i	0.0286311	+	0.162375i
$435$		0			0
$436$	−13.7121	+	4.99081i	−0.656692	+	0.239017i
$437$	−3.05797	−	2.56594i	−0.146283	−	0.122746i
$438$		0			0
$439$	−28.2935	−	10.2980i	−1.35038	−	0.491497i	−0.437312	−	0.899310i	$-0.644069\pi$
$439$	−28.2935	−	10.2980i	−1.35038	−	0.491497i	−0.913065	+	0.407813i	$0.866292\pi$
$440$	3.19685	+	5.53711i	0.152404	+	0.263971i
$441$		0			0
$442$	0.305914	−	0.529859i	0.0145508	−	0.0252028i
$443$	10.4654	−	8.78149i	0.497225	−	0.417221i	−0.359382	−	0.933191i	$-0.617013\pi$
$443$	10.4654	−	8.78149i	0.497225	−	0.417221i	0.856607	+	0.515969i	$0.172568\pi$
$444$		0			0
$445$	−4.89156	+	27.7414i	−0.231882	+	1.31507i
$446$	0.708226	−	4.01655i	0.0335355	−	0.190189i
$447$		0			0
$448$	−16.9312	+	14.2070i	−0.799925	+	0.671217i
$449$	10.9995	−	19.0516i	0.519097	−	0.899102i	−0.480657	−	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
$452$	17.3130	+	6.30142i	0.814335	+	0.296394i
$453$		0			0
$454$	−1.38922	−	1.16570i	−0.0651995	−	0.0547089i
$455$	−8.14433	+	2.96429i	−0.381812	+	0.138968i
$456$		0			0
$457$	−0.258532	−	1.46621i	−0.0120936	−	0.0685863i	0.978164	−	0.207836i	$-0.0666420\pi$
$457$	−0.258532	−	1.46621i	−0.0120936	−	0.0685863i	−0.990257	+	0.139250i	$0.955531\pi$
$458$	−2.40132			−0.112206
$459$		0			0
$460$	48.0281			2.23932
$461$	−1.23522	−	7.00527i	−0.0575298	−	0.326268i	0.942437	−	0.334383i	$-0.108528\pi$
$461$	−1.23522	−	7.00527i	−0.0575298	−	0.326268i	−0.999967	+	0.00811518i	$0.997417\pi$
$462$		0			0
$463$	24.9401	−	9.07746i	1.15907	−	0.421866i	0.310302	−	0.950638i	$-0.399570\pi$
$463$	24.9401	−	9.07746i	1.15907	−	0.421866i	0.848764	+	0.528772i	$0.177347\pi$
$464$	−19.1767	−	16.0912i	−0.890256	−	0.747013i
$465$		0			0
$466$	−1.23528	−	0.449605i	−0.0572232	−	0.0208275i
$467$	−13.0760	−	22.6482i	−0.605084	−	1.04804i	−0.992038	−	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
$470$	−0.548405	+	0.460166i	−0.0252960	+	0.0212259i
$471$		0			0
$472$	1.41331	−	8.01529i	0.0650529	−	0.368933i
$473$	−2.41027	+	13.6693i	−0.110824	+	0.628515i
$474$		0			0
$475$	−4.20044	+	3.52459i	−0.192729	+	0.161719i
$476$	13.8043	−	23.9098i	0.632719	−	1.09590i
$477$		0			0
$478$	−1.43213	−	2.48052i	−0.0655040	−	0.113456i
$479$	9.77896	+	3.55925i	0.446812	+	0.162626i	0.555620	−	0.831437i	$-0.312481\pi$
$479$	9.77896	+	3.55925i	0.446812	+	0.162626i	−0.108808	+	0.994063i	$0.534703\pi$
$480$		0			0
$481$	−2.90702	−	2.43928i	−0.132549	−	0.111222i
$482$	2.35990	−	0.858932i	0.107490	−	0.0391233i
$483$		0			0
$484$	1.63916	+	9.29613i	0.0745072	+	0.422551i
$485$	3.54358			0.160906
$486$		0			0
$487$	−18.4664			−0.836791			−0.418396	−	0.908265i	$-0.637407\pi$
$487$	−18.4664			−0.836791			−0.418396	+	0.908265i	$0.637407\pi$
$488$	−0.976293	−	5.53683i	−0.0441947	−	0.250641i
$489$		0			0
$490$	1.33010	−	0.484116i	0.0600877	−	0.0218701i
$491$	−13.0028	−	10.9106i	−0.586806	−	0.492389i	0.300368	−	0.953823i	$-0.402890\pi$
$491$	−13.0028	−	10.9106i	−0.586806	−	0.492389i	−0.887174	+	0.461435i	$0.847335\pi$
$492$		0			0
$493$	28.4570	+	10.3575i	1.28164	+	0.466479i
$494$	−0.0404890	−	0.0701289i	−0.00182168	−	0.00315525i
$495$		0			0
$496$	−12.5158	+	21.6780i	−0.561976	+	0.973371i
$497$	−11.4243	+	9.58611i	−0.512449	+	0.429996i
$498$		0			0
$499$	4.27976	−	24.2717i	0.191589	−	1.08655i	−0.725605	−	0.688111i	$-0.758440\pi$
$499$	4.27976	−	24.2717i	0.191589	−	1.08655i	0.917194	−	0.398441i	$-0.130449\pi$
$500$	5.06442	−	28.7218i	0.226488	−	1.28448i
$501$		0			0
$502$	1.19943	−	1.00644i	0.0535332	−	0.0449197i
$503$	−20.0569	+	34.7395i	−0.894291	+	1.54896i	−0.0596120	+	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
$506$	2.64244	+	0.961770i	0.117471	+	0.0427559i
$507$		0			0
$508$	−31.3859	−	26.3359i	−1.39252	−	1.16847i
$509$	−4.65009	+	1.69249i	−0.206111	+	0.0750184i	−0.443013	−	0.896515i	$-0.646090\pi$
$509$	−4.65009	+	1.69249i	−0.206111	+	0.0750184i	0.236901	+	0.971534i	$0.423868\pi$
$510$		0			0
$511$	2.26329	+	12.8358i	0.100122	+	0.567821i
$512$	13.0229			0.575537
$513$		0			0
$514$	1.67785			0.0740066
$515$	6.11540	+	34.6821i	0.269477	+	1.52828i
$516$		0			0
$517$	2.59340	−	0.943922i	0.114058	−	0.0415136i
$518$	1.99228	+	1.67172i	0.0875359	+	0.0734514i
$519$		0			0
$520$	1.84494	+	0.671505i	0.0809061	+	0.0294474i
$521$	−3.86979	−	6.70267i	−0.169539	−	0.293649i	0.768719	−	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	$0.878098\pi$
$524$	0.989757	−	0.830505i	0.0432378	−	0.0362808i
$525$		0			0
$526$	−0.806650	+	4.57474i	−0.0351716	+	0.199468i
$527$	5.25827	−	29.8212i	0.229054	−	1.29903i
$528$		0			0
$529$	14.9896	−	12.5777i	0.651720	−	0.546858i
$530$	2.85780	−	4.94986i	0.124135	−	0.215008i
$531$		0			0
$532$	−1.82705	−	3.16455i	−0.0792129	−	0.137201i
$533$	3.78209	+	1.37657i	0.163820	+	0.0596257i
$534$		0			0
$535$	3.65882	+	3.07011i	0.158184	+	0.132733i
$536$	−0.782338	+	0.284748i	−0.0337919	+	0.0122992i
$537$		0			0
$538$	0.352599	+	1.99969i	0.0152016	+	0.0862126i
$539$	−5.45676			−0.235039
$540$		0			0
$541$	−24.4147			−1.04967			−0.524834	−	0.851204i	$-0.675873\pi$
$541$	−24.4147			−1.04967			−0.524834	+	0.851204i	$0.675873\pi$
$542$	0.00434263	+	0.0246283i	0.000186532	+	0.00105787i
$543$		0			0
$544$	−8.83769	+	3.21666i	−0.378913	+	0.137913i
$545$	21.2013	+	17.7900i	0.908163	+	0.762039i
$546$		0			0
$547$	26.6514	+	9.70030i	1.13953	+	0.414755i	0.841743	−	0.539878i	$-0.181530\pi$
$547$	26.6514	+	9.70030i	1.13953	+	0.414755i	0.297786	+	0.954633i	$0.403752\pi$
$548$	8.45913	+	14.6516i	0.361356	+	0.625887i
$549$		0			0
$550$	1.93130	−	3.34512i	0.0823511	−	0.142636i
$551$	3.07040	−	2.57637i	0.130803	−	0.109757i
$552$		0			0
$553$	−6.20885	+	35.2121i	−0.264027	+	1.49737i
$554$	−0.0304702	+	0.172805i	−0.00129456	+	0.00734179i
$555$		0			0
$556$	−20.2925	+	17.0274i	−0.860593	+	0.722124i
$557$	18.4687	−	31.9887i	0.782542	−	1.35540i	−0.147914	−	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
$560$	40.6757	+	14.8047i	1.71886	+	0.625614i
$561$		0			0
$562$	−3.64785	−	3.06091i	−0.153875	−	0.129117i
$563$	−21.4019	+	7.78965i	−0.901982	+	0.328295i	−0.751047	−	0.660249i	$-0.770451\pi$
$563$	−21.4019	+	7.78965i	−0.901982	+	0.328295i	−0.150935	+	0.988544i	$0.548229\pi$
$564$		0			0
$565$	−6.06800	−	34.4133i	−0.255282	−	1.44778i
$566$	−4.63625			−0.194876
$567$		0			0
$568$	3.37833			0.141752
$569$	5.36030	+	30.3998i	0.224716	+	1.27443i	0.863228	+	0.504814i	$0.168439\pi$
$569$	5.36030	+	30.3998i	0.224716	+	1.27443i	−0.638512	+	0.769611i	$0.720450\pi$
$570$		0			0
$571$	−12.0473	+	4.38487i	−0.504165	+	0.183501i	−0.581566	−	0.813499i	$-0.697560\pi$
$571$	−12.0473	+	4.38487i	−0.504165	+	0.183501i	0.0774015	+	0.997000i	$0.475338\pi$
$572$	−2.87722	−	2.41427i	−0.120303	−	0.100946i
$573$		0			0
$574$	−2.59200	−	0.943409i	−0.108188	−	0.0393771i
$575$	−29.2354	−	50.6372i	−1.21920	−	2.11172i
$576$		0			0
$577$	11.7632	−	20.3745i	0.489708	−	0.848200i	−0.510222	−	0.860043i	$-0.670437\pi$
$577$	11.7632	−	20.3745i	0.489708	−	0.848200i	0.999930	+	0.0118433i	$0.00376992\pi$
$578$	0.579073	−	0.485900i	0.0240863	−	0.0202108i
$579$		0			0
$580$	−8.37388	+	47.4906i	−0.347706	+	1.97194i
$581$	4.74619	−	26.9170i	0.196905	−	1.11670i
$582$		0			0
$583$	−16.8793	+	14.1634i	−0.699068	+	0.586587i
$584$	1.47628	−	2.55699i	0.0610888	−	0.105809i
$585$		0			0
$586$	−1.61363	−	2.79489i	−0.0666584	−	0.115456i
$587$	−10.7007	−	3.89473i	−0.441665	−	0.160753i	0.111609	−	0.993752i	$-0.464400\pi$
$587$	−10.7007	−	3.89473i	−0.441665	−	0.160753i	−0.553274	+	0.832999i	$0.686622\pi$
$588$		0			0
$589$	−3.07018	−	2.57619i	−0.126505	−	0.106150i
$590$	−7.19824	+	2.61995i	−0.296347	+	0.107861i
$591$		0			0
$592$	3.29112	+	18.6649i	0.135264	+	0.767122i
$593$	−37.7324			−1.54948			−0.774742	−	0.632277i	$-0.782120\pi$
$593$	−37.7324			−1.54948			−0.774742	+	0.632277i	$0.782120\pi$
$594$		0			0
$595$	−52.3640			−2.14672
$596$	−3.29172	−	18.6682i	−0.134834	−	0.764681i
$597$		0			0
$598$	0.811429	−	0.295336i	0.0331818	−	0.0120772i
$599$	36.2785	+	30.4413i	1.48230	+	1.24380i	0.903687	+	0.428193i	$0.140850\pi$
$599$	36.2785	+	30.4413i	1.48230	+	1.24380i	0.578611	+	0.815604i	$0.303595\pi$
$600$		0			0
$601$	29.2314	+	10.6394i	1.19237	+	0.433989i	0.860557	−	0.509354i	$-0.170116\pi$
$601$	29.2314	+	10.6394i	1.19237	+	0.433989i	0.331818	+	0.943343i	$0.392338\pi$
$602$	−1.46054	−	2.52973i	−0.0595271	−	0.103104i
$603$		0			0
$604$	−7.02156	+	12.1617i	−0.285703	+	0.494853i
$605$	13.7149	−	11.5082i	0.557591	−	0.467874i
$606$		0			0
$607$	5.12027	−	29.0385i	0.207825	−	1.17864i	−0.685106	−	0.728443i	$-0.740244\pi$
$607$	5.12027	−	29.0385i	0.207825	−	1.17864i	0.892932	−	0.450192i	$-0.148645\pi$
$608$	−0.216153	+	1.22586i	−0.00876614	+	0.0497153i
$609$		0			0
$610$	−4.05356	+	3.40134i	−0.164124	+	0.137716i
$611$	0.423740	−	0.733939i	0.0171427	−	0.0296920i
$612$		0			0
$613$	3.05214	+	5.28646i	0.123275	+	0.213518i	0.921057	−	0.389427i	$-0.127327\pi$
$613$	3.05214	+	5.28646i	0.123275	+	0.213518i	−0.797782	+	0.602945i	$0.793994\pi$
$614$	−5.49225	−	1.99901i	−0.221649	−	0.0806737i
$615$		0			0
$616$	3.97366	+	3.33430i	0.160103	+	0.134343i
$617$	17.9670	−	6.53946i	0.723325	−	0.263269i	0.0459884	−	0.998942i	$-0.485356\pi$
$617$	17.9670	−	6.53946i	0.723325	−	0.263269i	0.677337	+	0.735673i	$0.263134\pi$
$618$		0			0
$619$	−1.17279	−	6.65125i	−0.0471386	−	0.267336i	0.952125	−	0.305709i	$-0.0988936\pi$
$619$	−1.17279	−	6.65125i	−0.0471386	−	0.267336i	−0.999263	+	0.0383731i	$0.987782\pi$
$620$	48.2198			1.93655
$621$		0			0
$622$	5.99994			0.240576
$623$	3.96856	+	22.5068i	0.158997	+	0.901716i
$624$		0			0
$625$	−9.87255	+	3.59331i	−0.394902	+	0.143733i
$626$	0.442625	+	0.371406i	0.0176908	+	0.0148444i
$627$		0			0
$628$	14.2284	+	5.17872i	0.567776	+	0.206654i
$629$	−11.4638	−	19.8559i	−0.457091	−	0.791705i
$630$		0			0
$631$	0.228453	−	0.395693i	0.00909458	−	0.0157523i	−0.861442	−	0.507855i	$-0.830438\pi$
$631$	0.228453	−	0.395693i	0.00909458	−	0.0157523i	0.870537	+	0.492103i	$0.163772\pi$
$632$	6.20472	−	5.20638i	0.246811	−	0.207099i
$633$		0			0
$634$	0.932131	−	5.28638i	0.0370196	−	0.209949i
$635$	−13.4940	+	76.5280i	−0.535491	+	3.03692i
$636$		0			0
$637$	−1.28361	+	1.07708i	−0.0508586	+	0.0426754i
$638$	−1.41173	+	2.44519i	−0.0558909	+	0.0968058i
$639$		0			0
$640$	−9.95805	−	17.2479i	−0.393627	−	0.681781i
$641$	−2.69789	−	0.981950i	−0.106560	−	0.0387847i	0.288190	−	0.957573i	$-0.406947\pi$
$641$	−2.69789	−	0.981950i	−0.106560	−	0.0387847i	−0.394750	+	0.918789i	$0.629169\pi$
$642$		0			0
$643$	−1.30445	−	1.09457i	−0.0514426	−	0.0431655i	0.616704	−	0.787195i	$-0.288468\pi$
$643$	−1.30445	−	1.09457i	−0.0514426	−	0.0431655i	−0.668146	+	0.744030i	$0.732912\pi$
$644$	36.6156	−	13.3270i	1.44286	−	0.525156i
$645$		0			0
$646$	−0.0849572	−	0.481816i	−0.00334260	−	0.0189568i
$647$	−36.1004			−1.41925			−0.709626	−	0.704579i	$-0.751136\pi$
$647$	−36.1004			−1.41925			−0.709626	+	0.704579i	$0.751136\pi$
$648$		0			0
$649$	29.5310			1.15919
$650$	−0.205966	−	1.16809i	−0.00807866	−	0.0458164i
$651$		0			0
$652$	1.93920	−	0.705812i	0.0759451	−	0.0276417i
$653$	33.3750	+	28.0050i	1.30606	+	1.09592i	0.989063	+	0.147494i	$0.0471206\pi$
$653$	33.3750	+	28.0050i	1.30606	+	1.09592i	0.317002	+	0.948425i	$0.397324\pi$
$654$		0			0
$655$	−2.30276	−	0.838137i	−0.0899764	−	0.0327487i
$656$	−10.0507	−	17.4083i	−0.392412	−	0.679678i
$657$		0			0
$658$	−0.290404	+	0.502994i	−0.0113211	+	0.0196087i
$659$	−19.5196	+	16.3789i	−0.760374	+	0.638030i	−0.938224	−	0.346028i	$-0.887530\pi$
$659$	−19.5196	+	16.3789i	−0.760374	+	0.638030i	0.177850	+	0.984058i	$0.443086\pi$
$660$		0			0
$661$	5.93307	−	33.6481i	0.230770	−	1.30876i	−0.620572	−	0.784149i	$-0.713100\pi$
$661$	5.93307	−	33.6481i	0.230770	−	1.30876i	0.851342	−	0.524611i	$-0.175789\pi$
$662$	0.0982712	−	0.557324i	0.00381942	−	0.0216610i
$663$		0			0
$664$	−4.74303	+	3.97988i	−0.184065	+	0.154449i
$665$	−3.46529	+	6.00207i	−0.134378	+	0.232750i
$666$		0			0
$667$	21.3702	+	37.0143i	0.827459	+	1.43320i
$668$	15.4656	+	5.62903i	0.598384	+	0.217794i
$669$		0			0
$670$	0.600255	+	0.503674i	0.0231899	+	0.0194586i
$671$	19.1693	−	6.97705i	0.740022	−	0.269346i
$672$		0			0
$673$	−5.13021	−	29.0949i	−0.197755	−	1.12153i	−0.908440	−	0.418015i	$-0.862726\pi$
$673$	−5.13021	−	29.0949i	−0.197755	−	1.12153i	0.710685	−	0.703511i	$-0.248385\pi$
$674$	1.10113			0.0424140
$675$		0			0
$676$	24.4577			0.940680
$677$	−7.08141	−	40.1607i	−0.272161	−	1.54350i	−0.747838	−	0.663881i	$-0.768908\pi$
$677$	−7.08141	−	40.1607i	−0.272161	−	1.54350i	0.475677	−	0.879620i	$-0.342203\pi$
$678$		0			0
$679$	2.70155	−	0.983285i	0.103676	−	0.0377350i
$680$	9.08688	+	7.62479i	0.348466	+	0.292398i
$681$		0			0
$682$	2.65299	+	0.965610i	0.101588	+	0.0369751i
$683$	15.8213	+	27.4033i	0.605384	+	1.04856i	0.991991	+	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
$686$	−1.93216	+	1.62128i	−0.0737704	+	0.0619007i
$687$		0			0
$688$	3.69649	−	20.9638i	0.140927	−	0.799238i
$689$	−1.17494	+	6.66340i	−0.0447616	+	0.253855i
$690$		0			0
$691$	−21.8972	+	18.3739i	−0.833008	+	0.698977i	−0.955980	−	0.293433i	$-0.905202\pi$
$691$	−21.8972	+	18.3739i	−0.833008	+	0.698977i	0.122971	+	0.992410i	$0.460758\pi$
$692$	21.5190	−	37.2719i	0.818028	−	1.41687i
$693$		0			0
$694$	−0.760438	−	1.31712i	−0.0288658	−	0.0499971i
$695$	47.2124	+	17.1839i	1.79087	+	0.651822i
$696$		0			0
$697$	18.6279	+	15.6306i	0.705581	+	0.592052i
$698$	−2.34067	+	0.851935i	−0.0885958	+	0.0322462i
$699$		0			0
$700$	−9.29418	−	52.7099i	−0.351287	−	1.99225i
$701$	7.52982			0.284397			0.142199	−	0.989838i	$-0.454583\pi$
$701$	7.52982			0.284397			0.142199	+	0.989838i	$0.454583\pi$
$702$		0			0
$703$	−3.03455			−0.114450
$704$	3.15459	+	17.8905i	0.118893	+	0.674275i
$705$		0			0
$706$	5.39655	−	1.96418i	0.203102	−	0.0739230i
$707$	−13.0236	−	10.9281i	−0.489803	−	0.410994i
$708$		0			0
$709$	−7.53069	−	2.74095i	−0.282821	−	0.102938i	0.196715	−	0.980461i	$-0.436973\pi$
$709$	−7.53069	−	2.74095i	−0.282821	−	0.102938i	−0.479536	+	0.877522i	$0.659195\pi$
$710$	−1.58981	−	2.75363i	−0.0596646	−	0.103342i
$711$		0			0
$712$	2.58857	−	4.48354i	0.0970108	−	0.168028i
$713$	32.7388	−	27.4711i	1.22608	−	1.02880i
$714$		0			0
$715$	−1.23702	+	7.01551i	−0.0462620	+	0.262365i
$716$	3.10924	−	17.6334i	0.116198	−	0.658990i
$717$		0			0
$718$	−0.655267	+	0.549835i	−0.0244544	+	0.0205196i
$719$	13.4913	−	23.3676i	0.503140	−	0.871464i	−0.496854	−	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
$722$	3.02749	+	1.10192i	0.112672	+	0.0410091i
$723$		0			0
$724$	10.7615	+	9.03000i	0.399949	+	0.335597i
$725$	55.1679	−	20.0795i	2.04888	−	0.745733i
$726$		0			0
$727$	−2.55164	−	14.4711i	−0.0946353	−	0.536703i	−0.994859	−	0.101275i	$-0.967708\pi$
$727$	−2.55164	−	14.4711i	−0.0946353	−	0.536703i	0.900223	−	0.435429i	$-0.143403\pi$
$728$	1.59288			0.0590360
$729$		0			0
$730$	−2.77889			−0.102851
$731$	4.47171	+	25.3603i	0.165392	+	0.937986i
$732$		0			0
$733$	29.4535	−	10.7202i	1.08789	−	0.395960i	0.265051	−	0.964234i	$-0.414611\pi$
$733$	29.4535	−	10.7202i	1.08789	−	0.395960i	0.822839	+	0.568275i	$0.192389\pi$
$734$	−0.330268	−	0.277128i	−0.0121904	−	0.0102290i
$735$		0			0
$736$	−12.4731	−	4.53984i	−0.459764	−	0.167341i
$737$	−1.51039	−	2.61607i	−0.0556359	−	0.0963642i
$738$		0			0
$739$	−0.241454	+	0.418211i	−0.00888205	+	0.0153842i	−0.870432	−	0.492288i	$-0.836161\pi$
$739$	−0.241454	+	0.418211i	−0.00888205	+	0.0153842i	0.861550	+	0.507672i	$0.169494\pi$
$740$	27.9682	−	23.4681i	1.02813	−	0.862704i
$741$		0			0
$742$	0.805225	−	4.56666i	0.0295608	−	0.167647i
$743$	−7.47568	+	42.3967i	−0.274256	+	1.55538i	0.467058	+	0.884226i	$0.345314\pi$
$743$	−7.47568	+	42.3967i	−0.274256	+	1.55538i	−0.741315	+	0.671158i	$0.765797\pi$
$744$		0			0
$745$	−27.5419	+	23.1104i	−1.00906	+	0.846701i
$746$	2.42578	−	4.20157i	0.0888140	−	0.153830i
$747$		0			0
$748$	−11.3462	−	19.6523i	−0.414860	−	0.718558i
$749$	3.64131	+	1.32533i	0.133051	+	0.0484264i
$750$		0			0
$751$	33.6459	+	28.2323i	1.22776	+	1.03021i	0.998381	+	0.0568722i	$0.0181127\pi$
$751$	33.6459	+	28.2323i	1.22776	+	1.03021i	0.229375	+	0.973338i	$0.426332\pi$
$752$	−3.97735	+	1.44764i	−0.145039	+	0.0527899i
$753$		0			0
$754$	0.150555	+	0.853843i	0.00548291	+	0.0310951i
$755$	26.6350			0.969346
$756$		0			0
$757$	22.4143			0.814661			0.407331	−	0.913281i	$-0.366460\pi$
$757$	22.4143			0.814661			0.407331	+	0.913281i	$0.366460\pi$
$758$	0.154387	+	0.875574i	0.00560760	+	0.0318023i
$759$		0			0
$760$	1.47531	−	0.536969i	0.0535152	−	0.0194779i
$761$	7.65795	+	6.42578i	0.277600	+	0.232934i	0.770948	−	0.636898i	$-0.219783\pi$
$761$	7.65795	+	6.42578i	0.277600	+	0.232934i	−0.493348	+	0.869832i	$0.664227\pi$
$762$		0			0
$763$	21.0998	+	7.67971i	0.763865	+	0.278024i
$764$	11.7768	+	20.3980i	0.426069	+	0.737972i
$765$		0			0
$766$	−0.00386367	+	0.00669207i	−0.000139600	+	0.000241794i
$767$	6.94667	−	5.82895i	0.250830	−	0.210471i
$768$		0			0
$769$	−1.30170	+	7.38231i	−0.0469405	+	0.266213i	−0.999241	−	0.0389483i	$-0.987599\pi$
$769$	−1.30170	+	7.38231i	−0.0469405	+	0.266213i	0.952301	+	0.305161i	$0.0987103\pi$
$770$	0.847775	−	4.80797i	0.0305517	−	0.173267i
$771$		0			0
$772$	13.3918	−	11.2371i	0.481982	−	0.404431i
$773$	−9.91954	+	17.1812i	−0.356781	+	0.617963i	−0.987421	−	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
$776$	−0.611986	−	0.222745i	−0.0219690	−	0.00799606i
$777$		0			0
$778$	−2.78030	−	2.33295i	−0.0996787	−	0.0836403i
$779$	3.02435	−	1.10077i	0.108359	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

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