LMFDB - Embedded newform 729.2.g.c.622.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			622.3
Character	$\chi$	$=$	729.622
Dual form			729.2.g.c.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.947282 + 1.00406i) q^{2} +(0.00549590 + 0.0943610i) q^{4} +(-4.01017 - 0.468722i) q^{5} +(-3.17727 + 1.59569i) q^{7} +(-2.21483 - 1.85846i) q^{8} +O(q^{10})$	\(q+(-0.947282 + 1.00406i) q^{2} +(0.00549590 + 0.0943610i) q^{4} +(-4.01017 - 0.468722i) q^{5} +(-3.17727 + 1.59569i) q^{7} +(-2.21483 - 1.85846i) q^{8} +(4.26939 - 3.58244i) q^{10} +(0.0643574 - 0.149197i) q^{11} +(0.339729 - 0.0805173i) q^{13} +(1.40761 - 4.70174i) q^{14} +(3.77632 - 0.441388i) q^{16} +(-0.388085 - 2.20094i) q^{17} +(-0.215481 + 1.22205i) q^{19} +(0.0221896 - 0.380980i) q^{20} +(0.0888384 + 0.205951i) q^{22} +(2.70748 + 1.35975i) q^{23} +(10.9966 + 2.60623i) q^{25} +(-0.240975 + 0.417381i) q^{26} +(-0.168033 - 0.291041i) q^{28} +(2.03874 + 6.80987i) q^{29} +(0.722935 - 0.475482i) q^{31} +(0.319024 - 0.428523i) q^{32} +(2.57750 + 1.69525i) q^{34} +(13.4893 - 4.90972i) q^{35} +(4.23271 + 1.54058i) q^{37} +(-1.02289 - 1.37399i) q^{38} +(8.01076 + 8.49090i) q^{40} +(-4.85103 - 5.14179i) q^{41} +(-5.63505 - 7.56918i) q^{43} +(0.0144321 + 0.00525286i) q^{44} +(-3.93001 + 1.43041i) q^{46} +(-3.65368 - 2.40306i) q^{47} +(3.36873 - 4.52499i) q^{49} +(-13.0337 + 8.57237i) q^{50} +(0.00946482 + 0.0316147i) q^{52} +(2.32646 + 4.02955i) q^{53} +(-0.328016 + 0.568141i) q^{55} +(10.0026 + 2.37067i) q^{56} +(-8.76878 - 4.40385i) q^{58} +(2.00630 + 4.65114i) q^{59} +(0.536580 - 9.21273i) q^{61} +(-0.207411 + 1.17629i) q^{62} +(1.44849 + 8.21478i) q^{64} +(-1.40011 + 0.163650i) q^{65} +(3.72757 - 12.4510i) q^{67} +(0.205550 - 0.0487163i) q^{68} +(-7.84856 + 18.1950i) q^{70} +(-1.23797 + 1.03878i) q^{71} +(-8.94621 - 7.50676i) q^{73} +(-5.55640 + 2.79053i) q^{74} +(-0.116499 - 0.0136167i) q^{76} +(0.0335910 + 0.576734i) q^{77} +(4.94986 - 5.24655i) q^{79} -15.3506 q^{80} +9.75795 q^{82} +(1.57700 - 1.67153i) q^{83} +(0.524660 + 9.00806i) q^{85} +(12.9379 + 1.51222i) q^{86} +(-0.419819 + 0.210841i) q^{88} +(8.92827 + 7.49171i) q^{89} +(-0.950932 + 0.797927i) q^{91} +(-0.113427 + 0.262953i) q^{92} +(5.87389 - 1.39214i) q^{94} +(1.43692 - 4.79965i) q^{95} +(4.17332 - 0.487791i) q^{97} +(1.35223 + 7.66885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−0.947282	+	1.00406i	−0.669829	+	0.709978i	−0.969781	−	0.243977i	$-0.921548\pi$
$2$	−0.947282	+	1.00406i	−0.669829	+	0.709978i	0.299952	+	0.953954i	$0.403029\pi$
$3$		0			0
$3$		0			0
$4$	0.00549590	+	0.0943610i	0.00274795	+	0.0471805i
$5$	−4.01017	−	0.468722i	−1.79340	−	0.209619i	−0.846777	−	0.531949i	$-0.821460\pi$
$5$	−4.01017	−	0.468722i	−1.79340	−	0.209619i	−0.946627	+	0.322330i	$0.895534\pi$
$6$		0			0
$7$	−3.17727	+	1.59569i	−1.20090	+	0.603113i	−0.932840	−	0.360291i	$-0.882677\pi$
$7$	−3.17727	+	1.59569i	−1.20090	+	0.603113i	−0.268056	+	0.963403i	$0.586381\pi$
$8$	−2.21483	−	1.85846i	−0.783061	−	0.657066i
$9$		0			0
$10$	4.26939	−	3.58244i	1.35010	−	1.13287i
$11$	0.0643574	−	0.149197i	0.0194045	−	0.0449847i	−0.908238	−	0.418453i	$-0.862572\pi$
$11$	0.0643574	−	0.149197i	0.0194045	−	0.0449847i	0.927643	+	0.373469i	$0.121832\pi$
$12$		0			0
$13$	0.339729	−	0.0805173i	0.0942240	−	0.0223315i	−0.183233	−	0.983069i	$-0.558656\pi$
$13$	0.339729	−	0.0805173i	0.0942240	−	0.0223315i	0.277457	+	0.960738i	$0.410508\pi$
$14$	1.40761	−	4.70174i	0.376199	−	1.25659i
$15$		0			0
$16$	3.77632	−	0.441388i	0.944079	−	0.110347i
$17$	−0.388085	−	2.20094i	−0.0941245	−	0.533807i	−0.995012	−	0.0997542i	$-0.968194\pi$
$17$	−0.388085	−	2.20094i	−0.0941245	−	0.533807i	0.900888	−	0.434053i	$-0.142917\pi$
$18$		0			0
$19$	−0.215481	+	1.22205i	−0.0494348	+	0.280358i	−0.999497	−	0.0317008i	$-0.989908\pi$
$19$	−0.215481	+	1.22205i	−0.0494348	+	0.280358i	0.950063	+	0.312059i	$0.101019\pi$
$20$	0.0221896	−	0.380980i	0.00496174	−	0.0851897i
$21$		0			0
$22$	0.0888384	+	0.205951i	0.0189404	+	0.0439088i
$23$	2.70748	+	1.35975i	0.564548	+	0.283527i	0.708095	−	0.706117i	$-0.249555\pi$
$23$	2.70748	+	1.35975i	0.564548	+	0.283527i	−0.143547	+	0.989643i	$0.545851\pi$
$24$		0			0
$25$	10.9966	+	2.60623i	2.19931	+	0.521247i
$26$	−0.240975	+	0.417381i	−0.0472591	+	0.0818552i
$27$		0			0
$28$	−0.168033	−	0.291041i	−0.0317552	−	0.0550016i
$29$	2.03874	+	6.80987i	0.378585	+	1.26456i	0.908990	+	0.416817i	$0.136854\pi$
$29$	2.03874	+	6.80987i	0.378585	+	1.26456i	−0.530406	+	0.847744i	$0.677960\pi$
$30$		0			0
$31$	0.722935	−	0.475482i	0.129843	−	0.0853991i	−0.482926	−	0.875661i	$-0.660426\pi$
$31$	0.722935	−	0.475482i	0.129843	−	0.0853991i	0.612769	+	0.790262i	$0.290056\pi$
$32$	0.319024	−	0.428523i	0.0563960	−	0.0757529i
$33$		0			0
$34$	2.57750	+	1.69525i	0.442038	+	0.290733i
$35$	13.4893	−	4.90972i	2.28012	−	0.829894i
$36$		0			0
$37$	4.23271	+	1.54058i	0.695853	+	0.253270i	0.665639	−	0.746274i	$-0.268159\pi$
$37$	4.23271	+	1.54058i	0.695853	+	0.253270i	0.0302136	+	0.999543i	$0.490381\pi$
$38$	−1.02289	−	1.37399i	−0.165935	−	0.222890i
$39$		0			0
$40$	8.01076	+	8.49090i	1.26661	+	1.34253i
$41$	−4.85103	−	5.14179i	−0.757603	−	0.803012i	0.227717	−	0.973727i	$-0.426874\pi$
$41$	−4.85103	−	5.14179i	−0.757603	−	0.803012i	−0.985320	+	0.170715i	$0.945392\pi$
$42$		0			0
$43$	−5.63505	−	7.56918i	−0.859336	−	1.15429i	−0.986719	−	0.162435i	$-0.948065\pi$
$43$	−5.63505	−	7.56918i	−0.859336	−	1.15429i	0.127383	−	0.991854i	$-0.459342\pi$
$44$	0.0144321	+	0.00525286i	0.00217572	+	0.000791898i
$45$		0			0
$46$	−3.93001	+	1.43041i	−0.579448	+	0.210902i
$47$	−3.65368	−	2.40306i	−0.532944	−	0.350523i	0.254338	−	0.967115i	$-0.418142\pi$
$47$	−3.65368	−	2.40306i	−0.532944	−	0.350523i	−0.787283	+	0.616592i	$0.788513\pi$
$48$		0			0
$49$	3.36873	−	4.52499i	0.481248	−	0.646428i
$50$	−13.0337	+	8.57237i	−1.84324	+	1.21232i
$51$		0			0
$52$	0.00946482	+	0.0316147i	0.00131253	+	0.00438417i
$53$	2.32646	+	4.02955i	0.319564	+	0.553502i	0.980397	−	0.197031i	$-0.0631301\pi$
$53$	2.32646	+	4.02955i	0.319564	+	0.553502i	−0.660833	+	0.750533i	$0.729797\pi$
$54$		0			0
$55$	−0.328016	+	0.568141i	−0.0442297	+	0.0766081i
$56$	10.0026	+	2.37067i	1.33666	+	0.316794i
$57$		0			0
$58$	−8.76878	−	4.40385i	−1.15140	−	0.578253i
$59$	2.00630	+	4.65114i	0.261199	+	0.605526i	0.997464	−	0.0711659i	$-0.0226720\pi$
$59$	2.00630	+	4.65114i	0.261199	+	0.605526i	−0.736266	+	0.676692i	$0.763413\pi$
$60$		0			0
$61$	0.536580	−	9.21273i	0.0687021	−	1.17957i	−0.771114	−	0.636698i	$-0.780300\pi$
$61$	0.536580	−	9.21273i	0.0687021	−	1.17957i	0.839816	−	0.542872i	$-0.182663\pi$
$62$	−0.207411	+	1.17629i	−0.0263412	+	0.149388i
$63$		0			0
$64$	1.44849	+	8.21478i	0.181061	+	1.02685i
$65$	−1.40011	+	0.163650i	−0.173663	+	0.0202983i
$66$		0			0
$67$	3.72757	−	12.4510i	0.455395	−	1.52113i	−0.354786	−	0.934947i	$-0.615446\pi$
$67$	3.72757	−	12.4510i	0.455395	−	1.52113i	0.810182	−	0.586179i	$-0.199368\pi$
$68$	0.205550	−	0.0487163i	0.0249266	−	0.00590772i
$69$		0			0
$70$	−7.84856	+	18.1950i	−0.938082	+	2.17472i
$71$	−1.23797	+	1.03878i	−0.146921	+	0.123281i	−0.713286	−	0.700874i	$-0.752794\pi$
$71$	−1.23797	+	1.03878i	−0.146921	+	0.123281i	0.566365	+	0.824155i	$0.308349\pi$
$72$		0			0
$73$	−8.94621	−	7.50676i	−1.04707	−	0.878600i	−0.0542914	−	0.998525i	$-0.517290\pi$
$73$	−8.94621	−	7.50676i	−1.04707	−	0.878600i	−0.992783	+	0.119925i	$0.961734\pi$
$74$	−5.55640	+	2.79053i	−0.645918	+	0.324392i
$75$		0			0
$76$	−0.116499	−	0.0136167i	−0.0133633	−	0.00156195i
$77$	0.0335910	+	0.576734i	0.00382805	+	0.0657250i
$78$		0			0
$79$	4.94986	−	5.24655i	0.556903	−	0.590283i	−0.386352	−	0.922351i	$-0.626265\pi$
$79$	4.94986	−	5.24655i	0.556903	−	0.590283i	0.943255	+	0.332068i	$0.107746\pi$
$80$	−15.3506			−1.71625
$81$		0			0
$82$	9.75795			1.07759
$83$	1.57700	−	1.67153i	0.173099	−	0.183474i	−0.635016	−	0.772499i	$-0.719007\pi$
$83$	1.57700	−	1.67153i	0.173099	−	0.183474i	0.808115	+	0.589025i	$0.200488\pi$
$84$		0			0
$85$	0.524660	+	9.00806i	0.0569073	+	0.977061i
$86$	12.9379	+	1.51222i	1.39513	+	0.163067i
$87$		0			0
$88$	−0.419819	+	0.210841i	−0.0447528	+	0.0224757i
$89$	8.92827	+	7.49171i	0.946395	+	0.794119i	0.978687	−	0.205359i	$-0.0658362\pi$
$89$	8.92827	+	7.49171i	0.946395	+	0.794119i	−0.0322920	+	0.999478i	$0.510281\pi$
$90$		0			0
$91$	−0.950932	+	0.797927i	−0.0996848	+	0.0836455i
$92$	−0.113427	+	0.262953i	−0.0118256	+	0.0274148i
$93$		0			0
$94$	5.87389	−	1.39214i	0.605845	−	0.143588i
$95$	1.43692	−	4.79965i	0.147425	−	0.492434i
$96$		0			0
$97$	4.17332	−	0.487791i	0.423736	−	0.0495277i	0.0984472	−	0.995142i	$-0.468612\pi$
$97$	4.17332	−	0.487791i	0.423736	−	0.0495277i	0.325289	+	0.945615i	$0.394538\pi$
$98$	1.35223	+	7.66885i	0.136595	+	0.774671i
$99$		0			0
$100$	−0.185491	+	1.05197i	−0.0185491	+	0.105197i
$101$	0.0974081	−	1.67243i	0.00969247	−	0.166413i	−0.989988	−	0.141149i	$-0.954920\pi$
$101$	0.0974081	−	1.67243i	0.00969247	−	0.166413i	0.999681	−	0.0252641i	$-0.00804267\pi$
$102$		0			0
$103$	1.33015	+	3.08363i	0.131064	+	0.303839i	0.971093	−	0.238701i	$-0.0767217\pi$
$103$	1.33015	+	3.08363i	0.131064	+	0.303839i	−0.840030	+	0.542541i	$0.817462\pi$
$104$	−0.902082	−	0.453043i	−0.0884564	−	0.0444245i
$105$		0			0
$106$	−6.24973	−	1.48121i	−0.607027	−	0.143868i
$107$	5.90368	−	10.2255i	0.570730	−	0.988534i	−0.425761	−	0.904836i	$-0.639993\pi$
$107$	5.90368	−	10.2255i	0.570730	−	0.988534i	0.996491	−	0.0836983i	$-0.0266732\pi$
$108$		0			0
$109$	5.03157	+	8.71493i	0.481937	+	0.834739i	0.999785	−	0.0207336i	$-0.00660019\pi$
$109$	5.03157	+	8.71493i	0.481937	+	0.834739i	−0.517848	+	0.855472i	$0.673267\pi$
$110$	−0.259724	−	0.867538i	−0.0247637	−	0.0827165i
$111$		0			0
$112$	−11.2941	+	7.42822i	−1.06719	+	0.701901i
$113$	2.33029	−	3.13013i	0.219215	−	0.294457i	−0.678888	−	0.734242i	$-0.737538\pi$
$113$	2.33029	−	3.13013i	0.219215	−	0.294457i	0.898103	+	0.439784i	$0.144945\pi$
$114$		0			0
$115$	−10.2201	−	6.72187i	−0.953030	−	0.626818i
$116$	−0.631382	+	0.229804i	−0.0586223	+	0.0213368i
$117$		0			0
$118$	−6.57056	−	2.39149i	−0.604869	−	0.220154i
$119$	4.74506	+	6.37373i	0.434979	+	0.584279i
$120$		0			0
$121$	7.53054	+	7.98191i	0.684595	+	0.725628i
$122$	8.74184	+	9.26581i	0.791449	+	0.838887i
$123$		0			0
$124$	0.0488401	+	0.0656037i	0.00438597	+	0.00589139i
$125$	−23.9066	−	8.70129i	−2.13827	−	0.778267i
$126$		0			0
$127$	−8.01819	+	2.91838i	−0.711499	+	0.258965i	−0.672313	−	0.740267i	$-0.734699\pi$
$127$	−8.01819	+	2.91838i	−0.711499	+	0.258965i	−0.0391867	+	0.999232i	$0.512477\pi$
$128$	−8.72756	−	5.74020i	−0.771414	−	0.507367i
$129$		0			0
$130$	1.16199	−	1.56082i	0.101913	−	0.136893i
$131$	13.5133	−	8.88786i	1.18066	−	0.776536i	0.201477	−	0.979493i	$-0.435426\pi$
$131$	13.5133	−	8.88786i	1.18066	−	0.776536i	0.979188	+	0.202958i	$0.0650554\pi$
$132$		0			0
$133$	−1.26537	−	4.22664i	−0.109722	−	0.366496i
$134$	8.97045	+	15.5373i	0.774929	+	1.34222i
$135$		0			0
$136$	−3.23083	+	5.59596i	−0.277041	+	0.479849i
$137$	−3.32647	−	0.788388i	−0.284200	−	0.0673566i	0.0860437	−	0.996291i	$-0.472578\pi$
$137$	−3.32647	−	0.788388i	−0.284200	−	0.0673566i	−0.370243	+	0.928935i	$0.620726\pi$
$138$		0			0
$139$	−10.0773	−	5.06102i	−0.854747	−	0.429270i	−0.0332254	−	0.999448i	$-0.510578\pi$
$139$	−10.0773	−	5.06102i	−0.854747	−	0.429270i	−0.821521	+	0.570178i	$0.806874\pi$
$140$	0.537422	+	1.24589i	0.0454205	+	0.105297i
$141$		0			0
$142$	0.129709	−	2.22702i	0.0108850	−	0.186888i
$143$	0.00985114	−	0.0558686i	0.000823793	−	0.00467196i
$144$		0			0
$145$	−4.98377	−	28.2644i	−0.413879	−	2.34723i
$146$	16.0118	−	1.87151i	1.32515	−	0.154887i
$147$		0			0
$148$	−0.122108	+	0.407870i	−0.0100372	+	0.0335267i
$149$	−0.581605	+	0.137843i	−0.0476470	+	0.0112925i	−0.254370	−	0.967107i	$-0.581868\pi$
$149$	−0.581605	+	0.137843i	−0.0476470	+	0.0112925i	0.206723	+	0.978399i	$0.433720\pi$
$150$		0			0
$151$	0.664309	−	1.54004i	0.0540607	−	0.125327i	−0.889045	−	0.457820i	$-0.848631\pi$
$151$	0.664309	−	1.54004i	0.0540607	−	0.125327i	0.943106	+	0.332493i	$0.107890\pi$
$152$	2.74840	−	2.30618i	0.222925	−	0.187056i
$153$		0			0
$154$	−0.610896	−	0.512603i	−0.0492274	−	0.0413067i
$155$	−3.12196	+	1.56791i	−0.250762	+	0.125937i
$156$		0			0
$157$	−9.06055	−	1.05903i	−0.723110	−	0.0845195i	−0.253427	−	0.967354i	$-0.581558\pi$
$157$	−9.06055	−	1.05903i	−0.723110	−	0.0845195i	−0.469683	+	0.882835i	$0.655632\pi$
$158$	0.578935	+	9.93992i	0.0460576	+	0.790778i
$159$		0			0
$160$	−1.48020	+	1.56892i	−0.117020	+	0.124034i
$161$	−10.7721			−0.848962
$162$		0			0
$163$	−21.8751			−1.71339			−0.856697	−	0.515821i	$-0.827487\pi$
$163$	−21.8751			−1.71339			−0.856697	+	0.515821i	$0.827487\pi$
$164$	0.458524	−	0.486007i	0.0358047	−	0.0379508i
$165$		0			0
$166$	0.184446	+	3.16681i	0.0143158	+	0.245792i
$167$	5.17360	+	0.604707i	0.400345	+	0.0467936i	0.313883	−	0.949462i	$-0.398370\pi$
$167$	5.17360	+	0.604707i	0.400345	+	0.0467936i	0.0864616	+	0.996255i	$0.472444\pi$
$168$		0			0
$169$	−11.5083	+	5.77968i	−0.885253	+	0.444591i
$170$	−9.54163	−	8.00638i	−0.731810	−	0.614061i
$171$		0			0
$172$	0.683266	−	0.573328i	0.0520985	−	0.0437159i
$173$	8.26239	−	19.1544i	0.628178	−	1.45628i	−0.245315	−	0.969444i	$-0.578891\pi$
$173$	8.26239	−	19.1544i	0.628178	−	1.45628i	0.873493	−	0.486837i	$-0.161849\pi$
$174$		0			0
$175$	−39.0978	+	9.26635i	−2.95552	+	0.700470i
$176$	0.177180	−	0.591823i	0.0133554	−	0.0446103i
$177$		0			0
$178$	−15.9797	+	1.86776i	−1.19773	+	0.139995i
$179$	−0.709018	−	4.02104i	−0.0529945	−	0.300547i	0.946778	−	0.321888i	$-0.104317\pi$
$179$	−0.709018	−	4.02104i	−0.0529945	−	0.300547i	−0.999772	+	0.0213413i	$0.993206\pi$
$180$		0			0
$181$	2.85517	−	16.1925i	0.212223	−	1.20358i	−0.673437	−	0.739244i	$-0.735183\pi$
$181$	2.85517	−	16.1925i	0.212223	−	1.20358i	0.885661	−	0.464333i	$-0.153706\pi$
$182$	0.0996343	−	1.71065i	0.00738538	−	0.126802i
$183$		0			0
$184$	−3.46957	−	8.04336i	−0.255780	−	0.592964i
$185$	−16.2518	−	8.16195i	−1.19485	−	0.600079i
$186$		0			0
$187$	−0.353351	−	0.0837456i	−0.0258396	−	0.00612409i
$188$	0.206675	−	0.357972i	0.0150734	−	0.0261078i
$189$		0			0
$190$	3.45797	+	5.98937i	0.250867	+	0.434515i
$191$	0.00119573	+	0.00399401i	8.65198e−5	+	0.000288996i	0.958033	−	0.286659i	$-0.0925446\pi$
$191$	0.00119573	+	0.00399401i	8.65198e−5	+	0.000288996i	−0.957946	+	0.286948i	$0.907359\pi$
$192$		0			0
$193$	17.5348	−	11.5328i	1.26218	−	0.830150i	0.270990	−	0.962582i	$-0.412649\pi$
$193$	17.5348	−	11.5328i	1.26218	−	0.830150i	0.991192	+	0.132432i	$0.0422785\pi$
$194$	−3.46354	+	4.65234i	−0.248667	+	0.334018i
$195$		0			0
$196$	0.445497	+	0.293008i	0.0318212	+	0.0209292i
$197$	−9.14507	+	3.32853i	−0.651559	+	0.237148i	−0.646588	−	0.762839i	$-0.723805\pi$
$197$	−9.14507	+	3.32853i	−0.651559	+	0.237148i	−0.00497138	+	0.999988i	$0.501582\pi$
$198$		0			0
$199$	22.6674	+	8.25026i	1.60685	+	0.584846i	0.980814	−	0.194948i	$-0.0624539\pi$
$199$	22.6674	+	8.25026i	1.60685	+	0.584846i	0.626036	+	0.779794i	$0.284676\pi$
$200$	−19.5119	−	26.2091i	−1.37970	−	1.85326i
$201$		0			0
$202$	1.58695	+	1.68207i	0.111657	+	0.118350i
$203$	−17.3440	−	18.3836i	−1.21731	−	1.29028i
$204$		0			0
$205$	17.0434	+	22.8932i	1.19036	+	1.59893i
$206$	−4.35618	−	1.58552i	−0.303509	−	0.110468i
$207$		0			0
$208$	1.24739	−	0.454011i	0.0864907	−	0.0314800i
$209$	0.168459	+	0.110797i	0.0116526	+	0.00766402i
$210$		0			0
$211$	8.98577	−	12.0700i	0.618606	−	0.830932i	−0.376838	−	0.926279i	$-0.622989\pi$
$211$	8.98577	−	12.0700i	0.618606	−	0.830932i	0.995444	+	0.0953471i	$0.0303961\pi$
$212$	−0.367447	+	0.241674i	−0.0252364	+	0.0165982i
$213$		0			0
$214$	4.67454	+	15.6141i	0.319545	+	1.06735i
$215$	19.0497	+	32.9950i	1.29918	+	2.25024i
$216$		0			0
$217$	−1.53824	+	2.66431i	−0.104423	+	0.180865i
$218$	−13.5166	−	3.20350i	−0.915461	−	0.216968i
$219$		0			0
$220$	−0.0554131	−	0.0278295i	−0.00373595	−	0.00187627i
$221$	−0.309058	−	0.716477i	−0.0207895	−	0.0481954i
$222$		0			0
$223$	−0.553847	+	9.50919i	−0.0370883	+	0.636782i	0.927630	+	0.373500i	$0.121842\pi$
$223$	−0.553847	+	9.50919i	−0.0370883	+	0.636782i	−0.964719	+	0.263283i	$0.915195\pi$
$224$	−0.329837	+	1.87060i	−0.0220381	+	0.124984i
$225$		0			0
$226$	0.935391	+	5.30486i	0.0622213	+	0.352874i
$227$	−12.1670	+	1.42212i	−0.807553	+	0.0943894i	−0.509843	−	0.860267i	$-0.670297\pi$
$227$	−12.1670	+	1.42212i	−0.807553	+	0.0943894i	−0.297709	+	0.954657i	$0.596223\pi$
$228$		0			0
$229$	−1.07081	+	3.57674i	−0.0707608	+	0.236358i	−0.986053	−	0.166434i	$-0.946775\pi$
$229$	−1.07081	+	3.57674i	−0.0707608	+	0.236358i	0.915292	+	0.402791i	$0.131960\pi$
$230$	16.4305	−	3.89410i	1.08339	−	0.256769i
$231$		0			0
$232$	8.14043	−	18.8716i	0.534446	−	1.23898i
$233$	15.7065	−	13.1793i	1.02896	−	0.863404i	0.0382373	−	0.999269i	$-0.487826\pi$
$233$	15.7065	−	13.1793i	1.02896	−	0.863404i	0.990727	+	0.135865i	$0.0433813\pi$
$234$		0			0
$235$	13.5255	+	11.3493i	0.882308	+	0.740344i
$236$	−0.427860	+	0.214879i	−0.0278513	+	0.0139874i
$237$		0			0
$238$	−10.8945	−	1.27339i	−0.706187	−	0.0825414i
$239$	0.753096	+	12.9302i	0.0487137	+	0.836382i	0.930853	+	0.365394i	$0.119066\pi$
$239$	0.753096	+	12.9302i	0.0487137	+	0.836382i	−0.882139	+	0.470989i	$0.843897\pi$
$240$		0			0
$241$	−8.32147	+	8.82024i	−0.536033	+	0.568162i	−0.937621	−	0.347659i	$-0.886977\pi$
$241$	−8.32147	+	8.82024i	−0.536033	+	0.568162i	0.401588	+	0.915820i	$0.368458\pi$
$242$	−15.1479			−0.973741
$243$		0			0
$244$	0.872272			0.0558415
$245$	−15.6302	+	16.5670i	−0.998575	+	1.05843i
$246$		0			0
$247$	0.0251913	+	0.432518i	0.00160288	+	0.0275204i
$248$	−2.48485	−	0.290437i	−0.157788	−	0.0184428i
$249$		0			0
$250$	31.3829	−	15.7611i	1.98483	−	0.996819i
$251$	−21.7457	−	18.2468i	−1.37257	−	1.15173i	−0.971869	−	0.235520i	$-0.924321\pi$
$251$	−21.7457	−	18.2468i	−1.37257	−	1.15173i	−0.400705	−	0.916207i	$-0.631235\pi$
$252$		0			0
$253$	0.377117	−	0.316438i	0.0237091	−	0.0198943i
$254$	4.66525	−	10.8153i	0.292724	−	0.678611i
$255$		0			0
$256$	−2.20235	+	0.521966i	−0.137647	+	0.0326229i
$257$	−7.88365	+	26.3332i	−0.491768	+	1.64262i	0.247262	+	0.968949i	$0.420469\pi$
$257$	−7.88365	+	26.3332i	−0.491768	+	1.64262i	−0.739031	+	0.673672i	$0.764716\pi$
$258$		0			0
$259$	−15.9067	+	1.85923i	−0.988397	+	0.115527i
$260$	−0.0231371	−	0.131217i	−0.00143490	−	0.00813772i
$261$		0			0
$262$	−3.87699	+	21.9875i	−0.239521	+	1.35839i
$263$	−0.270011	+	4.63592i	−0.0166496	+	0.285863i	0.979698	+	0.200477i	$0.0642493\pi$
$263$	−0.270011	+	4.63592i	−0.0166496	+	0.285863i	−0.996348	+	0.0853856i	$0.972788\pi$
$264$		0			0
$265$	−7.44078	−	17.2497i	−0.457084	−	1.05964i
$266$	5.44246	+	2.73331i	0.333699	+	0.167590i
$267$		0			0
$268$	1.19537	+	0.283308i	0.0730189	+	0.0173058i
$269$	2.50768	−	4.34343i	0.152896	−	0.264824i	−0.779395	−	0.626533i	$-0.784473\pi$
$269$	2.50768	−	4.34343i	0.152896	−	0.264824i	0.932291	+	0.361709i	$0.117807\pi$
$270$		0			0
$271$	−8.04356	−	13.9319i	−0.488612	−	0.846300i	0.511303	−	0.859401i	$-0.329163\pi$
$271$	−8.04356	−	13.9319i	−0.488612	−	0.846300i	−0.999914	+	0.0131007i	$0.995830\pi$
$272$	−2.43700	−	8.14015i	−0.147765	−	0.493569i
$273$		0			0
$274$	3.94270	−	2.59315i	0.238187	−	0.156658i
$275$	1.09655	−	1.47293i	0.0661246	−	0.0888208i
$276$		0			0
$277$	−8.22220	−	5.40783i	−0.494024	−	0.324925i	0.277932	−	0.960601i	$-0.410351\pi$
$277$	−8.22220	−	5.40783i	−0.494024	−	0.324925i	−0.771956	+	0.635676i	$0.780721\pi$
$278$	14.6276	−	5.32402i	0.877306	−	0.319313i
$279$		0			0
$280$	−39.0012	−	14.1953i	−2.33077	−	0.848329i
$281$	12.9836	+	17.4400i	0.774537	+	1.04038i	0.997844	+	0.0656355i	$0.0209075\pi$
$281$	12.9836	+	17.4400i	0.774537	+	1.04038i	−0.223307	+	0.974748i	$0.571685\pi$
$282$		0			0
$283$	3.29612	+	3.49368i	0.195934	+	0.207678i	0.817891	−	0.575374i	$-0.195143\pi$
$283$	3.29612	+	3.49368i	0.195934	+	0.207678i	−0.621956	+	0.783052i	$0.713662\pi$
$284$	−0.104825	−	0.111108i	−0.00622019	−	0.00659302i
$285$		0			0
$286$	0.0467636	+	0.0628144i	0.00276519	+	0.00371429i
$287$	23.6177	+	8.59614i	1.39411	+	0.507414i
$288$		0			0
$289$	11.2812	−	4.10604i	0.663602	−	0.241532i
$290$	33.1001	+	21.7703i	1.94371	+	1.27840i
$291$		0			0
$292$	0.659178	−	0.885430i	0.0385755	−	0.0518159i
$293$	4.72054	−	3.10475i	0.275777	−	0.181381i	−0.404085	−	0.914721i	$-0.632410\pi$
$293$	4.72054	−	3.10475i	0.275777	−	0.181381i	0.679862	+	0.733340i	$0.262040\pi$
$294$		0			0
$295$	−5.86554	−	19.5923i	−0.341505	−	1.14071i
$296$	−6.51162	−	11.2785i	−0.378480	−	0.655547i
$297$		0			0
$298$	0.412542	−	0.714543i	0.0238979	−	0.0413924i
$299$	1.02929	+	0.243947i	0.0595255	+	0.0141078i
$300$		0			0
$301$	29.9821	+	15.0576i	1.72814	+	0.867904i
$302$	0.917006	+	2.12586i	0.0527678	+	0.122329i
$303$		0			0
$304$	−0.274325	+	4.70997i	−0.0157336	+	0.270136i
$305$	−6.46999	+	36.6931i	−0.370470	+	2.10104i
$306$		0			0
$307$	1.38619	+	7.86146i	0.0791139	+	0.448677i	0.998472	+	0.0552559i	$0.0175975\pi$
$307$	1.38619	+	7.86146i	0.0791139	+	0.448677i	−0.919358	+	0.393421i	$0.871291\pi$
$308$	−0.0542367	+	0.00633936i	−0.00309042	+	0.000361218i
$309$		0			0
$310$	1.38310	−	4.61989i	0.0785550	−	0.262392i
$311$	−20.0883	+	4.76101i	−1.13910	+	0.269972i	−0.756534	−	0.653955i	$-0.773109\pi$
$311$	−20.0883	+	4.76101i	−1.13910	+	0.269972i	−0.382569	+	0.923927i	$0.624961\pi$
$312$		0			0
$313$	7.69699	−	17.8436i	0.435060	−	1.00858i	−0.549811	−	0.835289i	$-0.685300\pi$
$313$	7.69699	−	17.8436i	0.435060	−	1.00858i	0.984870	−	0.173293i	$-0.0554407\pi$
$314$	9.64622	−	8.09414i	0.544367	−	0.456779i
$315$		0			0
$316$	0.522274	+	0.438240i	0.0293802	+	0.0246529i
$317$	25.9928	−	13.0541i	1.45990	−	0.733189i	0.471050	−	0.882107i	$-0.343875\pi$
$317$	25.9928	−	13.0541i	1.45990	−	0.733189i	0.988850	+	0.148918i	$0.0475789\pi$
$318$		0			0
$319$	1.14722	+	0.134091i	0.0642321	+	0.00750766i
$320$	−1.95824	−	33.6216i	−0.109469	−	1.87951i
$321$		0			0
$322$	10.2042	−	10.8159i	0.568659	−	0.602744i
$323$	2.77330			0.154310
$324$		0			0
$325$	3.94570			0.218868
$326$	20.7219	−	21.9640i	1.14768	−	1.21647i
$327$		0			0
$328$	1.18838	+	20.4037i	0.0656172	+	1.12660i
$329$	15.4433	+	1.80506i	0.851415	+	0.0995162i
$330$		0			0
$331$	2.74452	−	1.37835i	0.150853	−	0.0757611i	−0.371771	−	0.928324i	$-0.621249\pi$
$331$	2.74452	−	1.37835i	0.150853	−	0.0757611i	0.522624	+	0.852563i	$0.324953\pi$
$332$	0.166394	+	0.139621i	0.00913206	+	0.00766271i
$333$		0			0
$334$	−5.50801	+	4.62177i	−0.301385	+	0.252892i
$335$	−20.7842	+	48.1833i	−1.13556	+	2.63253i
$336$		0			0
$337$	27.0527	−	6.41162i	1.47366	−	0.349263i	0.586205	−	0.810163i	$-0.300621\pi$
$337$	27.0527	−	6.41162i	1.47366	−	0.349263i	0.887452	+	0.460900i	$0.152473\pi$
$338$	5.09845	−	17.0300i	0.277319	−	0.926310i
$339$		0			0
$340$	−0.847126	+	0.0990149i	−0.0459419	+	0.00536984i
$341$	−0.0244144	−	0.138461i	−0.00132211	−	0.00749807i
$342$		0			0
$343$	0.838878	−	4.75751i	0.0452951	−	0.256882i
$344$	−1.58637	+	27.2370i	−0.0855316	+	1.46852i
$345$		0			0
$346$	11.4053	+	26.4405i	0.613154	+	1.42145i
$347$	−3.13174	−	1.57282i	−0.168120	−	0.0844332i	0.362749	−	0.931887i	$-0.381838\pi$
$347$	−3.13174	−	1.57282i	−0.168120	−	0.0844332i	−0.530869	+	0.847454i	$0.678135\pi$
$348$		0			0
$349$	−11.1318	−	2.63829i	−0.595874	−	0.141225i	−0.0783974	−	0.996922i	$-0.524980\pi$
$349$	−11.1318	−	2.63829i	−0.595874	−	0.141225i	−0.517476	+	0.855698i	$0.673128\pi$
$350$	27.7327	−	48.0344i	1.48237	−	2.56755i
$351$		0			0
$352$	−0.0434029	−	0.0751761i	−0.00231338	−	0.00400690i
$353$	0.526163	+	1.75751i	0.0280048	+	0.0935426i	0.970849	−	0.239690i	$-0.0770458\pi$
$353$	0.526163	+	1.75751i	0.0280048	+	0.0935426i	−0.942845	+	0.333233i	$0.891861\pi$
$354$		0			0
$355$	5.45139	−	3.58544i	0.289330	−	0.190295i
$356$	−0.657856	+	0.883655i	−0.0348663	+	0.0468336i
$357$		0			0
$358$	4.70901	+	3.09716i	0.248879	+	0.163690i
$359$	18.9025	−	6.87995i	0.997636	−	0.363110i	0.208964	−	0.977923i	$-0.432991\pi$
$359$	18.9025	−	6.87995i	0.997636	−	0.363110i	0.788673	+	0.614814i	$0.210769\pi$
$360$		0			0
$361$	16.4072	+	5.97172i	0.863536	+	0.314301i
$362$	13.5536	+	18.2056i	0.712360	+	0.956865i
$363$		0			0
$364$	−0.0805194	−	0.0853456i	−0.00422036	−	0.00447333i
$365$	32.3573	+	34.2967i	1.69366	+	1.79517i
$366$		0			0
$367$	15.7712	+	21.1845i	0.823252	+	1.10582i	0.992739	+	0.120287i	$0.0383816\pi$
$367$	15.7712	+	21.1845i	0.823252	+	1.10582i	−0.169487	+	0.985532i	$0.554211\pi$
$368$	10.8245	+	3.93978i	0.564264	+	0.205375i
$369$		0			0
$370$	23.5901	−	8.58610i	1.22639	−	0.446370i
$371$	−13.8217	−	9.09068i	−0.717587	−	0.471965i
$372$		0			0
$373$	−17.6990	+	23.7739i	−0.916420	+	1.23097i	0.0561660	+	0.998421i	$0.482112\pi$
$373$	−17.6990	+	23.7739i	−0.916420	+	1.23097i	−0.972586	+	0.232544i	$0.925295\pi$
$374$	0.418808	−	0.275455i	0.0216561	−	0.0142434i
$375$		0			0
$376$	3.62628	+	12.1126i	0.187011	+	0.624661i
$377$	1.24093	+	2.14936i	0.0639113	+	0.110698i
$378$		0			0
$379$	5.75292	−	9.96436i	0.295508	−	0.511835i	−0.679595	−	0.733587i	$-0.737844\pi$
$379$	5.75292	−	9.96436i	0.295508	−	0.511835i	0.975103	+	0.221753i	$0.0711778\pi$
$380$	0.460797	+	0.109211i	0.0236384	+	0.00560240i
$381$		0			0
$382$	−0.00514291	−	0.00258287i	−0.000263134	−	0.000132151i
$383$	−11.3929	−	26.4116i	−0.582149	−	1.34957i	−0.913798	−	0.406169i	$-0.866864\pi$
$383$	−11.3929	−	26.4116i	−0.582149	−	1.34957i	0.331649	−	0.943403i	$-0.392395\pi$
$384$		0			0
$385$	0.135623	−	2.32855i	0.00691197	−	0.118674i
$386$	−5.03075	+	28.5308i	−0.256059	+	1.45218i
$387$		0			0
$388$	0.0689646	+	0.391118i	0.00350115	+	0.0198560i
$389$	11.3779	−	1.32988i	0.576881	−	0.0674277i	0.177351	−	0.984148i	$-0.443247\pi$
$389$	11.3779	−	1.32988i	0.576881	−	0.0674277i	0.399530	+	0.916720i	$0.369173\pi$
$390$		0			0
$391$	1.94199	−	6.48669i	0.0982106	−	0.328046i
$392$	−15.8707	+	3.76143i	−0.801592	+	0.189981i
$393$		0			0
$394$	5.32091	−	12.3353i	0.268064	−	0.621441i
$395$	−22.3090	+	18.7195i	−1.12249	+	0.941878i
$396$		0			0
$397$	8.38197	+	7.03331i	0.420679	+	0.352992i	0.828421	−	0.560105i	$-0.189239\pi$
$397$	8.38197	+	7.03331i	0.420679	+	0.352992i	−0.407742	+	0.913097i	$0.633684\pi$
$398$	−29.7562	+	14.9441i	−1.49154	+	0.749081i
$399$		0			0
$400$	42.6769	+	4.98821i	2.13384	+	0.249410i
$401$	−0.0202092	−	0.346979i	−0.00100920	−	0.0173273i	0.997766	−	0.0668063i	$-0.0212810\pi$
$401$	−0.0202092	−	0.346979i	−0.00100920	−	0.0173273i	−0.998775	+	0.0494790i	$0.984244\pi$
$402$		0			0
$403$	0.207318	−	0.219744i	0.0103272	−	0.0109462i
$404$	0.158348			0.00787810
$405$		0			0
$406$	34.8880			1.73146
$407$	0.502256	−	0.532361i	0.0248959	−	0.0263881i
$408$		0			0
$409$	−1.54674	−	26.5565i	−0.0764813	−	1.31313i	−0.790264	−	0.612766i	$-0.790057\pi$
$409$	−1.54674	−	26.5565i	−0.0764813	−	1.31313i	0.713783	−	0.700367i	$-0.246980\pi$
$410$	−39.1311	−	4.57377i	−1.93255	−	0.225882i
$411$		0			0
$412$	−0.283664	+	0.142462i	−0.0139751	+	0.00701858i
$413$	−13.7963	−	11.5765i	−0.678873	−	0.569642i
$414$		0			0
$415$	−7.10754	+	5.96393i	−0.348895	+	0.292758i
$416$	0.0738782	−	0.171269i	0.00362218	−	0.00839715i
$417$		0			0
$418$	−0.270826	+	0.0641869i	−0.0132465	+	0.00313948i
$419$	−3.66857	+	12.2539i	−0.179221	+	0.598641i	0.820417	+	0.571765i	$0.193741\pi$
$419$	−3.66857	+	12.2539i	−0.179221	+	0.598641i	−0.999639	+	0.0268761i	$0.991444\pi$
$420$		0			0
$421$	10.8013	−	1.26249i	0.526424	−	0.0615302i	0.151270	−	0.988493i	$-0.451664\pi$
$421$	10.8013	−	1.26249i	0.526424	−	0.0615302i	0.375154	+	0.926962i	$0.377590\pi$
$422$	3.60693	+	20.4559i	0.175583	+	0.995779i
$423$		0			0
$424$	2.33606	−	13.2484i	0.113449	−	0.643401i
$425$	1.46856	−	25.2142i	0.0712357	−	1.22307i
$426$		0			0
$427$	12.9958	+	30.1276i	0.628909	+	1.45797i
$428$	0.997333	+	0.500879i	0.0482079	+	0.0242109i
$429$		0			0
$430$	−51.1743	−	12.1285i	−2.46785	−	0.584890i
$431$	1.22970	−	2.12989i	0.0592323	−	0.102593i	−0.834889	−	0.550419i	$-0.814468\pi$
$431$	1.22970	−	2.12989i	0.0592323	−	0.102593i	0.894121	+	0.447825i	$0.147801\pi$
$432$		0			0
$433$	6.44336	+	11.1602i	0.309648	+	0.536326i	0.978285	−	0.207263i	$-0.0664554\pi$
$433$	6.44336	+	11.1602i	0.309648	+	0.536326i	−0.668637	+	0.743589i	$0.733122\pi$
$434$	−1.21798	−	4.06834i	−0.0584650	−	0.195287i
$435$		0			0
$436$	−0.794697	+	0.522680i	−0.0380591	+	0.0250318i
$437$	−2.24509	+	3.01568i	−0.107397	+	0.144260i
$438$		0			0
$439$	23.0314	+	15.1480i	1.09923	+	0.722975i	0.963483	−	0.267769i	$-0.0862864\pi$
$439$	23.0314	+	15.1480i	1.09923	+	0.722975i	0.135746	+	0.990744i	$0.456657\pi$
$440$	1.78237	−	0.648730i	0.0849712	−	0.0309270i
$441$		0			0
$442$	1.01215	+	0.368393i	0.0481431	+	0.0175227i
$443$	3.42388	+	4.59907i	0.162673	+	0.218508i	0.875985	−	0.482339i	$-0.160213\pi$
$443$	3.42388	+	4.59907i	0.162673	+	0.218508i	−0.713311	+	0.700848i	$0.752805\pi$
$444$		0			0
$445$	−32.2924	−	34.2279i	−1.53081	−	1.62256i
$446$	−9.02315	−	9.56398i	−0.427258	−	0.452867i
$447$		0			0
$448$	−17.7104	−	23.7892i	−0.836740	−	1.12394i
$449$	−32.3537	−	11.7758i	−1.52687	−	0.555734i	−0.564015	−	0.825764i	$-0.690744\pi$
$449$	−32.3537	−	11.7758i	−1.52687	−	0.555734i	−0.962852	+	0.270030i	$0.912966\pi$
$450$		0			0
$451$	−1.07934	+	0.392848i	−0.0508242	+	0.0184985i
$452$	0.308169	+	0.202686i	0.0144951	+	0.00953354i
$453$		0			0
$454$	10.0977	−	13.5636i	0.473908	−	0.636569i
$455$	4.18741	−	2.75410i	0.196309	−	0.129114i
$456$		0			0
$457$	2.17602	+	7.26841i	0.101790	+	0.340002i	0.993680	−	0.112250i	$-0.0358059\pi$
$457$	2.17602	+	7.26841i	0.101790	+	0.340002i	−0.891890	+	0.452252i	$0.850621\pi$
$458$	−2.57691	−	4.46333i	−0.120411	−	0.208558i
$459$		0			0
$460$	0.578114	−	1.00132i	0.0269547	−	0.0466869i
$461$	−1.79155	−	0.424604i	−0.0834406	−	0.0197758i	0.188683	−	0.982038i	$-0.439578\pi$
$461$	−1.79155	−	0.424604i	−0.0834406	−	0.0197758i	−0.272124	+	0.962262i	$0.587726\pi$
$462$		0			0
$463$	−20.1099	−	10.0996i	−0.934588	−	0.469368i	−0.0847444	−	0.996403i	$-0.527007\pi$
$463$	−20.1099	−	10.0996i	−0.934588	−	0.469368i	−0.849844	+	0.527035i	$0.823304\pi$
$464$	10.7047	+	24.8163i	0.496954	+	1.15207i
$465$		0			0
$466$	−1.64565	+	28.2547i	−0.0762333	+	1.30888i
$467$	6.84563	−	38.8235i	0.316778	−	1.79654i	−0.245292	−	0.969449i	$-0.578884\pi$
$467$	6.84563	−	38.8235i	0.316778	−	1.79654i	0.562071	−	0.827089i	$-0.310005\pi$
$468$		0			0
$469$	8.02431	+	45.5081i	0.370528	+	2.10137i
$470$	−24.2078	+	2.82949i	−1.11662	+	0.130515i
$471$		0			0
$472$	4.20035	−	14.0301i	0.193337	−	0.645789i
$473$	−1.49196	+	0.353600i	−0.0686003	+	0.0162586i
$474$		0			0
$475$	−5.55451	+	12.8768i	−0.254858	+	0.590828i
$476$	−0.575353	+	0.482779i	−0.0263713	+	0.0221281i
$477$		0			0
$478$	−13.6960	−	11.4923i	−0.626443	−	0.525648i
$479$	−2.35856	+	1.18451i	−0.107765	+	0.0541217i	−0.501865	−	0.864946i	$-0.667353\pi$
$479$	−2.35856	+	1.18451i	−0.107765	+	0.0541217i	0.394100	+	0.919068i	$0.371056\pi$
$480$		0			0
$481$	1.56202	+	0.182574i	0.0712219	+	0.00832465i
$482$	−0.973276	−	16.7105i	−0.0443315	−	0.761143i
$483$		0			0
$484$	−0.711794	+	0.754457i	−0.0323543	+	0.0342935i
$485$	−16.9644			−0.770312
$486$		0			0
$487$	−25.0040			−1.13304			−0.566519	−	0.824048i	$-0.691710\pi$
$487$	−25.0040			−1.13304			−0.566519	+	0.824048i	$0.691710\pi$
$488$	−18.3100	+	19.4074i	−0.828853	+	0.878533i
$489$		0			0
$490$	−1.82810	−	31.3872i	−0.0825851	−	1.41793i
$491$	−29.9031	−	3.49517i	−1.34951	−	0.157735i	−0.589563	−	0.807723i	$-0.700700\pi$
$491$	−29.9031	−	3.49517i	−1.34951	−	0.157735i	−0.759944	+	0.649988i	$0.774774\pi$
$492$		0			0
$493$	14.1969	−	7.12996i	0.639397	−	0.321117i
$494$	−0.458137	−	0.384423i	−0.0206126	−	0.0172960i
$495$		0			0
$496$	2.52016	−	2.11466i	0.113158	−	0.0949512i
$497$	2.27581	−	5.27592i	0.102084	−	0.236657i
$498$		0			0
$499$	−5.48586	+	1.30017i	−0.245581	+	0.0582037i	−0.351563	−	0.936164i	$-0.614350\pi$
$499$	−5.48586	+	1.30017i	−0.245581	+	0.0582037i	0.105982	+	0.994368i	$0.466201\pi$
$500$	0.689674	−	2.30367i	0.0308432	−	0.103023i
$501$		0			0
$502$	38.9202	−	4.54911i	1.73709	−	0.203037i
$503$	2.01083	+	11.4040i	0.0896587	+	0.508479i	0.996254	+	0.0864779i	$0.0275612\pi$
$503$	2.01083	+	11.4040i	0.0896587	+	0.508479i	−0.906595	+	0.422002i	$0.861328\pi$
$504$		0			0
$505$	−1.17453	+	6.66108i	−0.0522659	+	0.296414i
$506$	−0.0395125	+	0.678404i	−0.00175655	+	0.0301587i
$507$		0			0
$508$	−0.319449	−	0.740566i	−0.0141732	−	0.0328573i
$509$	32.0484	+	16.0953i	1.42052	+	0.713413i	0.982623	−	0.185611i	$-0.0594265\pi$
$509$	32.0484	+	16.0953i	1.42052	+	0.713413i	0.437899	+	0.899024i	$0.355723\pi$
$510$		0			0
$511$	40.4030	+	9.57568i	1.78732	+	0.423603i
$512$	12.0082	−	20.7988i	0.530693	−	0.919188i
$513$		0			0
$514$	−18.9721	−	32.8606i	−0.836823	−	1.44942i
$515$	−3.88876	−	12.9894i	−0.171359	−	0.572380i
$516$		0			0
$517$	−0.593672	+	0.390464i	−0.0261097	+	0.0171726i
$518$	13.2014	−	17.7325i	0.580036	−	0.779123i
$519$		0			0
$520$	3.40515	+	2.23960i	0.149326	+	0.0982132i
$521$	8.36834	−	3.04583i	0.366624	−	0.133440i	−0.152137	−	0.988359i	$-0.548616\pi$
$521$	8.36834	−	3.04583i	0.366624	−	0.133440i	0.518761	+	0.854919i	$0.326393\pi$
$522$		0			0
$523$	−15.1809	−	5.52540i	−0.663815	−	0.241609i	−0.0119324	−	0.999929i	$-0.503798\pi$
$523$	−15.1809	−	5.52540i	−0.663815	−	0.241609i	−0.651883	+	0.758320i	$0.726021\pi$
$524$	0.912935	+	1.22628i	0.0398818	+	0.0535705i
$525$		0			0
$526$	−4.39896	−	4.66263i	−0.191804	−	0.203300i
$527$	−1.32707	−	1.40661i	−0.0578080	−	0.0612729i
$528$		0			0
$529$	−8.25313	−	11.0859i	−0.358832	−	0.481995i
$530$	24.3682	+	8.86931i	1.05849	+	0.385258i
$531$		0			0
$532$	0.391876	−	0.142631i	0.0169900	−	0.00618384i
$533$	−2.06204	−	1.35622i	−0.0893168	−	0.0587446i
$534$		0			0
$535$	−28.4677	+	38.2387i	−1.23077	+	1.65321i
$536$	−31.3956	+	20.6492i	−1.35608	+	0.891910i
$537$		0			0
$538$	1.98559	+	6.63232i	0.0856047	+	0.285940i
$539$	−0.458314	−	0.793823i	−0.0197410	−	0.0341924i
$540$		0			0
$541$	4.75257	−	8.23170i	0.204329	−	0.353908i	−0.745590	−	0.666405i	$-0.767832\pi$
$541$	4.75257	−	8.23170i	0.204329	−	0.353908i	0.949919	+	0.312497i	$0.101165\pi$
$542$	21.6079	+	5.12118i	0.928140	+	0.219973i
$543$		0			0
$544$	−1.06696	−	0.535849i	−0.0457457	−	0.0229743i
$545$	−16.0926	−	37.3068i	−0.689330	−	1.59805i
$546$		0			0
$547$	−0.308516	+	5.29702i	−0.0131912	+	0.226484i	0.985269	+	0.171012i	$0.0547036\pi$
$547$	−0.308516	+	5.29702i	−0.0131912	+	0.226484i	−0.998460	+	0.0554726i	$0.982333\pi$
$548$	0.0561112	−	0.318222i	0.00239695	−	0.0135938i
$549$		0			0
$550$	0.440162	+	2.49628i	0.0187686	+	0.106442i
$551$	−8.76134	+	1.02405i	−0.373246	+	0.0436262i
$552$		0			0
$553$	−7.35522	+	24.5681i	−0.312776	+	1.04474i
$554$	13.2185	−	3.13285i	0.561601	−	0.133102i
$555$		0			0
$556$	0.422179	−	0.978721i	0.0179044	−	0.0415070i
$557$	25.1867	−	21.1341i	1.06719	−	0.895481i	0.0723978	−	0.997376i	$-0.476935\pi$
$557$	25.1867	−	21.1341i	1.06719	−	0.895481i	0.994795	+	0.101895i	$0.0324904\pi$
$558$		0			0
$559$	−2.52384	−	2.11775i	−0.106747	−	0.0895714i
$560$	48.7729	−	24.4947i	2.06103	−	1.03509i
$561$		0			0
$562$	−29.8099	−	3.48428i	−1.25746	−	0.146976i
$563$	−0.742347	−	12.7456i	−0.0312862	−	0.537163i	−0.977144	−	0.212581i	$-0.931813\pi$
$563$	−0.742347	−	12.7456i	−0.0312862	−	0.537163i	0.945857	−	0.324583i	$-0.105224\pi$
$564$		0			0
$565$	−10.8120	+	11.4601i	−0.454866	+	0.482130i
$566$	−6.63022			−0.278689
$567$		0			0
$568$	4.67245			0.196052
$569$	29.4927	−	31.2604i	1.23640	−	1.31050i	0.302419	−	0.953175i	$-0.402206\pi$
$569$	29.4927	−	31.2604i	1.23640	−	1.31050i	0.933979	−	0.357329i	$-0.116313\pi$
$570$		0			0
$571$	0.221256	+	3.79881i	0.00925926	+	0.158975i	0.999768	+	0.0215274i	$0.00685292\pi$
$571$	0.221256	+	3.79881i	0.00925926	+	0.158975i	−0.990509	+	0.137448i	$0.956110\pi$
$572$	0.00532596		0.000622515i	0.000222689		2.60287e-5i
$573$		0			0
$574$	−31.0037	+	15.5706i	−1.29407	+	0.649905i
$575$	26.2291	+	22.0088i	1.09383	+	0.917832i
$576$		0			0
$577$	11.5311	−	9.67573i	0.480045	−	0.402806i	−0.370397	−	0.928873i	$-0.620779\pi$
$577$	11.5311	−	9.67573i	0.480045	−	0.402806i	0.850443	+	0.526067i	$0.176334\pi$
$578$	−6.56381	+	15.2166i	−0.273018	+	0.632928i
$579$		0			0
$580$	2.63966	−	0.625612i	0.109606	−	0.0259771i
$581$	−2.34334	+	7.82729i	−0.0972181	+	0.324731i
$582$		0			0
$583$	0.750924	−	0.0877704i	0.0311001	−	0.00363508i
$584$	5.86330	+	33.2524i	0.242625	+	1.37599i
$585$		0			0
$586$	−1.35433	+	7.68078i	−0.0559468	+	0.317290i
$587$	2.21700	−	38.0644i	0.0915054	−	1.57109i	−0.570316	−	0.821425i	$-0.693179\pi$
$587$	2.21700	−	38.0644i	0.0915054	−	1.57109i	0.661822	−	0.749661i	$-0.269784\pi$
$588$		0			0
$589$	0.425286	+	0.985923i	0.0175236	+	0.0406243i
$590$	25.2281	+	12.6700i	1.03863	+	0.521617i
$591$		0			0
$592$	16.6640	+	3.94945i	0.684888	+	0.162321i
$593$	5.81375	−	10.0697i	0.238742	−	0.413513i	−0.721612	−	0.692298i	$-0.756598\pi$
$593$	5.81375	−	10.0697i	0.238742	−	0.413513i	0.960354	+	0.278785i	$0.0899317\pi$
$594$		0			0
$595$	−16.0410	−	27.7839i	−0.657618	−	1.13903i
$596$	−0.0162035	−	0.0541233i	−0.000663720	−	0.00221698i
$597$		0			0
$598$	−1.21997	+	0.802385i	−0.0498882	+	0.0328120i
$599$	−24.1107	+	32.3863i	−0.985136	+	1.32327i	−0.0390903	+	0.999236i	$0.512446\pi$
$599$	−24.1107	+	32.3863i	−0.985136	+	1.32327i	−0.946046	+	0.324032i	$0.894961\pi$
$600$		0			0
$601$	16.4724	+	10.8341i	0.671925	+	0.441932i	0.839087	−	0.543998i	$-0.183090\pi$
$601$	16.4724	+	10.8341i	0.671925	+	0.441932i	−0.167162	+	0.985929i	$0.553460\pi$
$602$	−43.5202	+	15.8401i	−1.77375	+	0.645593i
$603$		0			0
$604$	0.148971	+	0.0542210i	0.00606154	+	0.00220622i
$605$	−26.4575	−	35.5386i	−1.07565	−	1.44485i
$606$		0			0
$607$	−1.26194	−	1.33758i	−0.0512205	−	0.0542906i	0.701257	−	0.712909i	$-0.252623\pi$
$607$	−1.26194	−	1.33758i	−0.0512205	−	0.0542906i	−0.752477	+	0.658618i	$0.771141\pi$
$608$	0.454935	+	0.482203i	0.0184501	+	0.0195559i
$609$		0			0
$610$	−30.7132	−	41.2550i	−1.24354	−	1.67037i
$611$	−1.43475	−	0.522207i	−0.0580438	−	0.0211262i
$612$		0			0
$613$	−33.2921	+	12.1173i	−1.34465	+	0.489414i	−0.911275	−	0.411797i	$-0.864901\pi$
$613$	−33.2921	+	12.1173i	−1.34465	+	0.489414i	−0.433379	+	0.901212i	$0.642679\pi$
$614$	−9.20649	−	6.05520i	−0.371544	−	0.244368i
$615$		0			0
$616$	0.997442	−	1.33980i	0.0401881	−	0.0539820i
$617$	31.0126	−	20.3973i	1.24852	−	0.821165i	0.259045	−	0.965865i	$-0.416592\pi$
$617$	31.0126	−	20.3973i	1.24852	−	0.821165i	0.989476	+	0.144700i	$0.0462217\pi$
$618$		0			0
$619$	−9.74402	−	32.5473i	−0.391645	−	1.30819i	−0.895755	−	0.444547i	$-0.853365\pi$
$619$	−9.74402	−	32.5473i	−0.391645	−	1.30819i	0.504110	−	0.863639i	$-0.331821\pi$
$620$	−0.165108	−	0.285975i	−0.00663088	−	0.0114850i
$621$		0			0
$622$	14.2489	−	24.6799i	0.571330	−	0.989573i
$623$	−40.3220	−	9.55648i	−1.61546	−	0.382872i
$624$		0			0
$625$	41.2956	+	20.7394i	1.65182	+	0.829577i
$626$	10.6249	+	24.6312i	0.424655	+	0.984461i
$627$		0			0
$628$	0.0501349	−	0.860783i	0.00200060	−	0.0343490i
$629$	1.74807	−	9.91382i	0.0697003	−	0.395290i
$630$		0			0
$631$	−1.91892	−	10.8828i	−0.0763912	−	0.433236i	−0.998884	−	0.0472226i	$-0.984963\pi$
$631$	−1.91892	−	10.8828i	−0.0763912	−	0.433236i	0.922493	−	0.386013i	$-0.126148\pi$
$632$	−20.7136	+	2.42108i	−0.823945	+	0.0963053i
$633$		0			0
$634$	−11.5154	+	38.4642i	−0.457336	+	1.52761i
$635$	33.5222	−	7.94492i	1.33029	−	0.315284i
$636$		0			0
$637$	0.780117	−	1.80851i	0.0309094	−	0.0716560i
$638$	−1.22138	+	1.02486i	−0.0483548	+	0.0405745i
$639$		0			0
$640$	32.3085	+	27.1100i	1.27710	+	1.07162i
$641$	14.5321	−	7.29830i	0.573984	−	0.288265i	−0.138033	−	0.990428i	$-0.544078\pi$
$641$	14.5321	−	7.29830i	0.573984	−	0.288265i	0.712017	+	0.702162i	$0.247782\pi$
$642$		0			0
$643$	−14.1768	−	1.65703i	−0.559078	−	0.0653468i	−0.168139	−	0.985763i	$-0.553776\pi$
$643$	−14.1768	−	1.65703i	−0.559078	−	0.0653468i	−0.390939	+	0.920416i	$0.627850\pi$
$644$	−0.0592025	−	1.01647i	−0.00233291	−	0.0400545i
$645$		0			0
$646$	−2.62709	+	2.78455i	−0.103362	+	0.109557i
$647$	−40.7899			−1.60362			−0.801808	−	0.597582i	$-0.796128\pi$
$647$	−40.7899			−1.60362			−0.801808	+	0.597582i	$0.796128\pi$
$648$		0			0
$649$	0.823057			0.0323078
$650$	−3.73769	+	3.96172i	−0.146604	+	0.155391i
$651$		0			0
$652$	−0.120224	−	2.06416i	−0.00470832	−	0.0808388i
$653$	−2.55616	−	0.298772i	−0.100030	−	0.0116918i	0.0659306	−	0.997824i	$-0.478998\pi$
$653$	−2.55616	−	0.298772i	−0.100030	−	0.0116918i	−0.165961	+	0.986132i	$0.553072\pi$
$654$		0			0
$655$	−58.3567	+	29.3078i	−2.28019	+	1.14515i
$656$	−20.5885	−	17.2758i	−0.803847	−	0.674508i
$657$		0			0
$658$	−16.4415	+	13.7961i	−0.640957	+	0.537827i
$659$	−3.40053	+	7.88331i	−0.132466	+	0.307090i	−0.971520	−	0.236958i	$-0.923850\pi$
$659$	−3.40053	+	7.88331i	−0.132466	+	0.307090i	0.839054	+	0.544048i	$0.183109\pi$
$660$		0			0
$661$	36.0921	−	8.55398i	1.40382	−	0.332711i	0.542192	−	0.840254i	$-0.317594\pi$
$661$	36.0921	−	8.55398i	1.40382	−	0.332711i	0.861626	+	0.507543i	$0.169446\pi$
$662$	−1.21589	+	4.06135i	−0.0472569	+	0.157849i
$663$		0			0
$664$	−6.59927	+	0.771344i	−0.256101	+	0.0299340i
$665$	3.09324	+	17.5427i	0.119951	+	0.680275i
$666$		0			0
$667$	−3.73985	+	21.2097i	−0.144807	+	0.821244i
$668$	−0.0286272	+	0.491509i	−0.00110762	+	0.0190171i
$669$		0			0
$670$	−28.6904	−	66.5118i	−1.10841	−	2.56957i
$671$	−1.33998	−	0.672964i	−0.0517294	−	0.0259795i
$672$		0			0
$673$	21.5825	+	5.11516i	0.831946	+	0.197175i	0.624454	−	0.781062i	$-0.285322\pi$
$673$	21.5825	+	5.11516i	0.831946	+	0.197175i	0.207492	+	0.978237i	$0.433470\pi$
$674$	−19.1889	+	33.2362i	−0.739130	+	1.28021i
$675$		0			0
$676$	−0.608625	−	1.05417i	−0.0234087	−	0.0405450i
$677$	−1.24236	−	4.14976i	−0.0477477	−	0.159488i	0.930791	−	0.365552i	$-0.119120\pi$
$677$	−1.24236	−	4.14976i	−0.0477477	−	0.159488i	−0.978539	+	0.206064i	$0.933935\pi$
$678$		0			0
$679$	−12.4814	+	8.20915i	−0.478992	+	0.315038i
$680$	15.5791	−	20.9264i	0.597432	−	0.802491i
$681$		0			0
$682$	0.162150	+	0.106648i	0.00620905	+	0.00408376i
$683$	−38.0275	+	13.8409i	−1.45508	+	0.529607i	−0.944006	−	0.329928i	$-0.892976\pi$
$683$	−38.0275	+	13.8409i	−1.45508	+	0.529607i	−0.511077	+	0.859535i	$0.670753\pi$
$684$		0			0
$685$	12.9702	+	4.72076i	0.495566	+	0.180371i
$686$	3.98217	+	5.34899i	0.152040	+	0.204225i
$687$		0			0
$688$	−24.6207	−	26.0964i	−0.938654	−	0.994915i
$689$	1.11482	+	1.18164i	0.0424711	+	0.0450168i
$690$		0			0
$691$	−13.9201	−	18.6980i	−0.529547	−	0.711305i	0.454193	−	0.890903i	$-0.349928\pi$
$691$	−13.9201	−	18.6980i	−0.529547	−	0.711305i	−0.983740	+	0.179598i	$0.942520\pi$
$692$	1.85284	+	0.674377i	0.0704343	+	0.0256360i
$693$		0			0
$694$	4.54584	−	1.65455i	0.172558	−	0.0628058i
$695$	38.0396	+	25.0190i	1.44292	+	0.949025i
$696$		0			0
$697$	−9.43416	+	12.6723i	−0.357344	+	0.479997i
$698$	13.1940	−	8.67783i	0.499400	−	0.328461i
$699$		0			0
$700$	−1.08926	−	3.63838i	−0.0411702	−	0.137518i
$701$	−5.97599	−	10.3507i	−0.225710	−	0.390941i	0.730822	−	0.682568i	$-0.239137\pi$
$701$	−5.97599	−	10.3507i	−0.225710	−	0.390941i	−0.956532	+	0.291627i	$0.905804\pi$
$702$		0			0
$703$	−2.79474	+	4.84063i	−0.105406	+	0.182568i
$704$	1.31884	+	0.312572i	0.0497058	+	0.0117805i
$705$		0			0
$706$	−2.26307	−	1.13655i	−0.0851716	−	0.0427748i
$707$	2.35918	+	5.46920i	0.0887263	+	0.205691i
$708$		0			0
$709$	0.831035	−	14.2683i	0.0312102	−	0.535858i	−0.946077	−	0.323941i	$-0.894992\pi$
$709$	0.831035	−	14.2683i	0.0312102	−	0.535858i	0.977288	−	0.211918i	$-0.0679708\pi$
$710$	−1.56401	+	8.86995i	−0.0586963	+	0.332883i
$711$		0			0
$712$	−5.85154	−	33.1857i	−0.219296	−	1.24369i
$713$	2.60386	−	0.304348i	0.0975155	−	0.0113979i
$714$		0			0
$715$	−0.0656916	+	0.219425i	−0.00245673	+	0.00820604i
$716$	0.375533	−	0.0890029i	0.0140343	−	0.00332620i
$717$		0			0
$718$	−10.9981	+	25.4965i	−0.410446	+	0.951521i
$719$	−10.2202	+	8.57578i	−0.381150	+	0.319823i	−0.813154	−	0.582049i	$-0.802251\pi$
$719$	−10.2202	+	8.57578i	−0.381150	+	0.319823i	0.432004	+	0.901872i	$0.357807\pi$
$720$		0			0
$721$	−9.14676	−	7.67504i	−0.340643	−	0.285833i
$722$	−21.5382	+	10.8169i	−0.801568	+	0.402563i
$723$		0			0
$724$	1.54363	+	0.180425i	0.0573686	+	0.00670543i
$725$	4.67104	+	80.1986i	0.173478	+	2.97850i
$726$		0			0
$727$	−28.2910	+	29.9867i	−1.04925	+	1.11214i	−0.0557382	+	0.998445i	$0.517751\pi$
$727$	−28.2910	+	29.9867i	−1.04925	+	1.11214i	−0.993515	+	0.113698i	$0.963730\pi$
$728$	3.58907			0.133020
$729$		0			0
$730$	−65.0874			−2.40899
$731$	−14.4724	+	15.3399i	−0.535283	+	0.567366i
$732$		0			0
$733$	−0.675142	−	11.5917i	−0.0249369	−	0.428151i	−0.987554	−	0.157283i	$-0.949726\pi$
$733$	−0.675142	−	11.5917i	−0.0249369	−	0.428151i	0.962617	−	0.270868i	$-0.0873106\pi$
$734$	−36.2103	−	4.23238i	−1.33655	−	0.156220i
$735$		0			0
$736$	1.44643	−	0.726425i	0.0533162	−	0.0267764i
$737$	−1.61775	−	1.35745i	−0.0595907	−	0.0500025i
$738$		0			0
$739$	−27.7185	+	23.2586i	−1.01964	+	0.855581i	−0.989582	−	0.143968i	$-0.954014\pi$
$739$	−27.7185	+	23.2586i	−1.01964	+	0.855581i	−0.0300588	+	0.999548i	$0.509569\pi$
$740$	0.680852	−	1.57839i	0.0250286	−	0.0580229i
$741$		0			0
$742$	22.2206	−	5.26639i	0.815745	−	0.193335i
$743$	14.5076	−	48.4588i	0.532233	−	1.77778i	−0.0911193	−	0.995840i	$-0.529044\pi$
$743$	14.5076	−	48.4588i	0.532233	−	1.77778i	0.623352	−	0.781941i	$-0.285770\pi$
$744$		0			0
$745$	2.39695	−	0.280163i	0.0878174	−	0.0102644i
$746$	−7.10447	−	40.2914i	−0.260113	−	1.47517i
$747$		0			0
$748$	0.00596034	−	0.0338028i	0.000217932	−	0.00123595i
$749$	−2.44095	+	41.9095i	−0.0891905	+	1.53134i
$750$		0			0
$751$	15.9854	+	37.0582i	0.583314	+	1.35227i	0.912913	+	0.408154i	$0.133827\pi$
$751$	15.9854	+	37.0582i	0.583314	+	1.35227i	−0.329599	+	0.944121i	$0.606914\pi$
$752$	−14.8581	−	7.46204i	−0.541821	−	0.272113i
$753$		0			0
$754$	−3.33360	−	0.790077i	−0.121402	−	0.0287729i
$755$	−3.38584	+	5.86446i	−0.123224	+	0.213429i
$756$		0			0
$757$	23.2499	+	40.2700i	0.845032	+	1.46364i	0.885593	+	0.464462i	$0.153752\pi$
$757$	23.2499	+	40.2700i	0.845032	+	1.46364i	−0.0405607	+	0.999177i	$0.512914\pi$
$758$	4.55517	+	15.2153i	0.165451	+	0.552646i
$759$		0			0
$760$	−12.1025	+	7.95995i	−0.439004	+	0.288738i
$761$	−4.01868	+	5.39803i	−0.145677	+	0.195678i	−0.868972	−	0.494860i	$-0.835219\pi$
$761$	−4.01868	+	5.39803i	−0.145677	+	0.195678i	0.723295	+	0.690539i	$0.242627\pi$
$762$		0			0
$763$	−29.8929	−	19.6609i	−1.08220	−	0.711772i
$764$	−0.000370307	0	0.000134781i	−1.33972e−5	0	4.87620e-6i
$765$		0			0
$766$	37.3111	+	13.5801i	1.34811	+	0.490671i
$767$	1.05610	+	1.41859i	0.0381335	+	0.0512221i
$768$		0			0
$769$	−17.9772	−	19.0547i	−0.648273	−	0.687129i	0.316984	−	0.948431i	$-0.397330\pi$
$769$	−17.9772	−	19.0547i	−0.648273	−	0.687129i	−0.965257	+	0.261302i	$0.915848\pi$
$770$	2.20953	+	2.34197i	0.0796260	+	0.0843986i
$771$		0			0
$772$	1.18462	+	1.59122i	0.0426353	+	0.0572692i
$773$	15.5434	+	5.65735i	0.559059	+	0.203481i	0.606067	−	0.795414i	$-0.292746\pi$
$773$	15.5434	+	5.65735i	0.559059	+	0.203481i	−0.0470079	+	0.998895i	$0.514969\pi$
$774$		0			0
$775$	9.18902	−	3.34453i	0.330079	−	0.120139i
$776$	−10.1497	−	6.67559i	−0.364355	−	0.239640i
$777$		0			0
$778$	−9.44276	+	12.6838i	−0.338539	+	0.454737i
$779$	7.32885	−	4.82026i	0.262583	−	0.172704i
$780$		0			0
$781$	0.0753109	+	0.251556i	0.00269484	+	0.00900138i
$782$	4.67342	+	8.09460i	0.167121	+	0.289462i
$783$		0			0
$784$	10.7241	−	18.5747i	0.383004	−	0.663383i
$785$	35.8380	+	8.49376i	1.27911	+	0.303155i
$786$		0			0
$787$	−12.0313	−	6.04235i	−0.428870	−	0.215387i	0.221252	−	0.975217i	$-0.428986\pi$
$787$	−12.0313	−	6.04235i	−0.428870	−	0.215387i	−0.650122	+	0.759830i	$0.725282\pi$
$788$	−0.364344	−	0.844645i	−0.0129792	−	0.0300892i
$789$		0			0
$790$	2.33743	−	40.1322i	0.0831621	−	1.42784i
$791$	−2.40927	+	13.6637i	−0.0856640	+	0.485824i
$792$		0			0
$793$	−0.559492	−	3.17304i	−0.0198682	−	0.112678i
$794$	−15.0020	+	1.75348i	−0.532399	+	0.0622286i
$795$		0			0
$796$	−0.653925	+	2.18426i	−0.0231778	+	0.0774191i
$797$	−0.482674	+	0.114396i	−0.0170972	+	0.00405211i	−0.239156	−	0.970981i	$-0.576871\pi$
$797$	−0.482674	+	0.114396i	−0.0170972	+	0.00405211i	0.222058	+	0.975033i	$0.428722\pi$
$798$		0			0
$799$	−3.87106	+	8.97414i	−0.136948	+	0.317482i
$800$	4.62500	−	3.88083i	0.163518	−	0.137208i
$801$		0			0
$802$	0.367532	+	0.308396i	0.0129780	+	0.0108898i
$803$	−1.69574	+	0.851634i	−0.0598415	+	0.0300535i
$804$		0			0
$805$	43.1980	+	5.04913i	1.52253	+	0.177958i
$806$	0.0242478	+	0.416319i	0.000854093	+	0.0146642i
$807$		0			0
$808$	−3.32390	+	3.52313i	−0.116934	+	0.123943i
$809$	20.5900			0.723906			0.361953	−	0.932196i	$-0.382110\pi$
$809$	20.5900			0.723906			0.361953	+	0.932196i	$0.382110\pi$
$810$		0			0
$811$	27.9946			0.983022			0.491511	−	0.870871i	$-0.336445\pi$
$811$	27.9946			0.983022			0.491511	+	0.870871i	$0.336445\pi$
$812$	1.63938	−	1.73764i	0.0575308	−	0.0609791i
$813$		0			0
$814$	0.0587437	+	1.00859i	0.00205897	+	0.0353511i
$815$	87.7231	+	10.2534i	3.07281	+	0.359160i
$816$		0			0
$817$	10.4642	−	5.25532i	0.366096	−	0.183860i
$818$	28.1295	+	23.6035i	0.983525	+	0.825275i
$819$		0			0
$820$	−2.06656	+	1.73405i	−0.0721675	+	0.0605557i
$821$	17.5567	−	40.7011i	0.612735	−	1.42048i	−0.275596	−	0.961274i	$-0.588875\pi$
$821$	17.5567	−	40.7011i	0.612735	−	1.42048i	0.888330	−	0.459205i	$-0.151866\pi$
$822$		0			0
$823$	−13.5565	+	3.21296i	−0.472551	+	0.111997i	−0.459990	−	0.887924i	$-0.652147\pi$
$823$	−13.5565	+	3.21296i	−0.472551	+	0.111997i	−0.0125620	+	0.999921i	$0.503999\pi$
$824$	2.78477	−	9.30177i	0.0970119	−	0.324042i
$825$		0			0
$826$	24.6925	−	2.88614i	0.859162	−	0.100422i
$827$	−1.96973	−	11.1709i	−0.0684943	−	0.388451i	−0.999712	−	0.0239878i	$-0.992364\pi$
$827$	−1.96973	−	11.1709i	−0.0684943	−	0.388451i	0.931218	−	0.364463i	$-0.118747\pi$
$828$		0			0
$829$	6.55402	−	37.1697i	0.227630	−	1.29096i	−0.629962	−	0.776626i	$-0.716929\pi$
$829$	6.55402	−	37.1697i	0.227630	−	1.29096i	0.857592	−	0.514330i	$-0.171959\pi$
$830$	0.744695	−	12.7859i	0.0258487	−	0.443806i
$831$		0			0
$832$	1.15353	+	2.67417i	0.0399913	+	0.0927102i
$833$	−11.2666	−	5.65830i	−0.390365	−	0.196048i
$834$		0			0
$835$	−20.4636	−	4.84996i	−0.708171	−	0.167840i
$836$	−0.00952913	+	0.0165049i	−0.000329572	+	0.000570835i
$837$		0			0
$838$	−8.82846	−	15.2913i	−0.304974	−	0.528231i
$839$	−8.17364	−	27.3019i	−0.282185	−	0.942565i	−0.975141	−	0.221585i	$-0.928877\pi$
$839$	−8.17364	−	27.3019i	−0.282185	−	0.942565i	0.692956	−	0.720980i	$-0.256308\pi$
$840$		0			0
$841$	−17.9887	+	11.8314i	−0.620300	+	0.407978i
$842$	−8.96427	+	12.0411i	−0.308929	+	0.414964i
$843$		0			0
$844$	1.18832	+	0.781571i	0.0409037	+	0.0269028i
$845$	48.8593	−	17.7833i	1.68081	−	0.611765i
$846$		0			0
$847$	−36.6632	−	13.3443i	−1.25976	−	0.458516i
$848$	10.5641	+	14.1900i	0.362771	+	0.487286i
$849$		0			0
$850$	23.9255	+	25.3595i	0.820637	+	0.869824i
$851$	9.36516	+	9.92649i	0.321034	+	0.340276i
$852$		0			0
$853$	−16.9871	−	22.8176i	−0.581627	−	0.781261i	0.409765	−	0.912191i	$-0.365611\pi$
$853$	−16.9871	−	22.8176i	−0.581627	−	0.781261i	−0.991392	+	0.130931i	$0.958203\pi$
$854$	−42.5605	−	15.4908i	−1.45639	−	0.530083i
$855$		0			0
$856$	−32.0793	+	11.6759i	−1.09645	+	0.399075i
$857$	−13.5990	−	8.94422i	−0.464534	−	0.305529i	0.295581	−	0.955318i	$-0.404487\pi$
$857$	−13.5990	−	8.94422i	−0.464534	−	0.305529i	−0.760115	+	0.649789i	$0.774857\pi$
$858$		0			0
$859$	33.9028	−	45.5394i	1.15675	−	1.55378i	0.378775	−	0.925489i	$-0.376346\pi$
$859$	33.9028	−	45.5394i	1.15675	−	1.55378i	0.777975	−	0.628295i	$-0.216247\pi$
$860$	−3.00875	+	1.97888i	−0.102597	+	0.0674794i
$861$		0			0
$862$	0.973674	+	3.25230i	0.0331635	+	0.110774i
$863$	3.57676	+	6.19512i	0.121754	+	0.210884i	0.920460	−	0.390838i	$-0.127815\pi$
$863$	3.57676	+	6.19512i	0.121754	+	0.210884i	−0.798705	+	0.601722i	$0.794481\pi$
$864$		0			0
$865$	−42.1117	+	72.9396i	−1.43184	+	2.48002i
$866$	−17.3092	−	4.10236i	−0.588191	−	0.139404i
$867$		0			0
$868$	−0.259861	−	0.130507i	−0.00882027	−	0.00442971i
$869$	−0.464210	−	1.07616i	−0.0157473	−	0.0365063i
$870$		0			0
$871$	0.263848	−	4.53009i	0.00894014	−	0.153496i
$872$	5.05231	−	28.6531i	0.171093	−	0.970316i
$873$		0			0
$874$	−0.901191	−	5.11091i	−0.0304833	−	0.172879i
$875$	89.8423	−	10.5011i	3.03722	−	0.355001i
$876$		0			0
$877$	−5.31635	+	17.7578i	−0.179520	+	0.599639i	0.820104	+	0.572215i	$0.193916\pi$
$877$	−5.31635	+	17.7578i	−0.179520	+	0.599639i	−0.999624	+	0.0274244i	$0.991269\pi$
$878$	−37.0267	+	8.77550i	−1.24959	+	0.296159i
$879$		0			0
$880$	−0.987923	+	2.29026i	−0.0333029	+	0.0772047i
$881$	−35.8699	+	30.0984i	−1.20849	+	1.01404i	−0.209142	+	0.977885i	$0.567067\pi$
$881$	−35.8699	+	30.0984i	−1.20849	+	1.01404i	−0.999346	+	0.0361571i	$0.988488\pi$
$882$		0			0
$883$	−35.2742	−	29.5986i	−1.18707	−	0.996071i	−0.999906	−	0.0137426i	$-0.995625\pi$
$883$	−35.2742	−	29.5986i	−1.18707	−	0.996071i	−0.187166	−	0.982328i	$-0.559930\pi$
$884$	0.0659089	−	0.0331007i	0.00221676	−	0.00111330i
$885$		0			0
$886$	−7.86112	−	0.918833i	−0.264100	−	0.0308688i
$887$	−0.213648	−	3.66819i	−0.00717360	−	0.123166i	−0.999994	−	0.00354886i	$-0.998870\pi$
$887$	−0.213648	−	3.66819i	−0.00717360	−	0.123166i	0.992820	−	0.119617i	$-0.0381667\pi$
$888$		0			0
$889$	20.8191	−	22.0670i	0.698252	−	0.740104i
$890$	64.9569			2.17736
$891$		0			0
$892$	−0.900341			−0.0301456
$893$	3.72398	−	3.94718i	0.124618	−	0.132087i
$894$		0			0
$895$	0.958535	+	16.4574i	0.0320403	+	0.550110i
$896$	36.8894	+	4.31175i	1.23239	+	0.144045i
$897$		0			0
$898$	42.4717	−	21.3301i	1.41730	−	0.711794i
$899$	4.71185	+	3.95371i	0.157149	+	0.131864i
$900$		0			0
$901$	7.96595	−	6.68422i	0.265384	−	0.222684i
$902$	0.627997	−	1.45586i	0.0209100	−	0.0484748i
$903$		0			0
$904$	−10.9784	+	2.60194i	−0.365137	+	0.0865391i
$905$	−19.0395	+	63.5964i	−0.632894	+	2.11401i
$906$		0			0
$907$	−13.5107	+	1.57917i	−0.448614	+	0.0524355i	−0.337401	−	0.941361i	$-0.609548\pi$
$907$	−13.5107	+	1.57917i	−0.448614	+	0.0524355i	−0.111213	+	0.993797i	$0.535474\pi$
$908$	−0.201061	−	1.14028i	−0.00667246	−	0.0378414i
$909$		0			0
$910$	−1.20137	+	6.81332i	−0.0398251	+	0.225859i
$911$	0.263485	−	4.52387i	0.00872965	−	0.149882i	−0.991127	−	0.132922i	$-0.957564\pi$
$911$	0.263485	−	4.52387i	0.00872965	−	0.149882i	0.999856	−	0.0169604i	$-0.00539892\pi$
$912$		0			0
$913$	−0.147895	−	0.342860i	−0.00489462	−	0.0113470i
$914$	−9.35922	−	4.70038i	−0.309575	−	0.155475i
$915$		0			0
$916$	−0.343390	−	0.0813849i	−0.0113459	−	0.00268903i
$917$	−28.7533	+	49.8022i	−0.949517	+	1.64461i
$918$		0			0
$919$	12.4131	+	21.5002i	0.409472	+	0.709226i	0.994831	−	0.101548i	$-0.0323796\pi$
$919$	12.4131	+	21.5002i	0.409472	+	0.709226i	−0.585359	+	0.810775i	$0.699046\pi$
$920$	10.1435	+	33.8815i	0.334420	+	1.11704i
$921$		0			0
$922$	2.12343	−	1.39660i	0.0699314	−	0.0459946i
$923$	−0.336936	+	0.452584i	−0.0110904	+	0.0148970i
$924$		0			0
$925$	42.5301	+	27.9725i	1.39838	+	0.919730i
$926$	29.1904	−	10.6244i	0.959255	−	0.349140i
$927$		0			0
$928$	3.56859	+	1.29886i	0.117145	+	0.0426372i
$929$	7.72102	+	10.3711i	0.253319	+	0.340266i	0.910532	−	0.413439i	$-0.135672\pi$
$929$	7.72102	+	10.3711i	0.253319	+	0.340266i	−0.657213	+	0.753705i	$0.728265\pi$
$930$		0			0
$931$	4.80389	+	5.09183i	0.157441	+	0.166878i
$932$	1.32993	+	1.40965i	0.0435634	+	0.0461745i
$933$		0			0
$934$	32.4964	+	43.6502i	1.06331	+	1.42828i
$935$	1.37774	+	0.501458i	0.0450570	+	0.0163994i
$936$		0			0
$937$	54.1109	−	19.6948i	1.76773	−	0.643400i	0.767729	−	0.640774i	$-0.221387\pi$
$937$	54.1109	−	19.6948i	1.76773	−	0.643400i	0.999997	−	0.00262511i	$-0.000835598\pi$
$938$	−53.2941	−	35.0521i	−1.74012	−	1.14449i
$939$		0			0
$940$	−0.996593	+	1.33866i	−0.0325053	+	0.0436622i
$941$	13.7882	−	9.06863i	0.449482	−	0.295629i	−0.304514	−	0.952508i	$-0.598494\pi$
$941$	13.7882	−	9.06863i	0.449482	−	0.295629i	0.753996	+	0.656879i	$0.228124\pi$
$942$		0			0
$943$	−6.14252	−	20.5174i	−0.200028	−	0.668140i
$944$	9.62940	+	16.6786i	0.313410	+	0.542842i
$945$		0			0
$946$	1.05827	−	1.83297i	0.0344073	−	0.0595951i
$947$	17.6535	+	4.18395i	0.573661	+	0.135960i	0.507199	−	0.861829i	$-0.330681\pi$
$947$	17.6535	+	4.18395i	0.573661	+	0.135960i	0.0664619	+	0.997789i	$0.478829\pi$
$948$		0			0
$949$	−3.64371	−	1.82994i	−0.118280	−	0.0594024i
$950$	−7.66740	−	17.7750i	−0.248763	−	0.576698i
$951$		0			0
$952$	1.33583	−	22.9353i	0.0432944	−	0.743336i
$953$	−4.36891	+	24.7773i	−0.141523	+	0.802616i	0.828571	+	0.559885i	$0.189155\pi$
$953$	−4.36891	+	24.7773i	−0.141523	+	0.802616i	−0.970094	+	0.242732i	$0.921957\pi$
$954$		0			0
$955$	−0.00292299	−	0.0165771i	−9.45859e−5	−	0.000536423i
$956$	−1.21596	+	0.142126i	−0.0393271	+	0.00459668i
$957$		0			0
$958$	1.04490	−	3.49020i	0.0337591	−	0.112763i
$959$	11.8271	−	2.80308i	0.381918	−	0.0905162i
$960$		0			0
$961$	−11.9819	+	27.7772i	−0.386514	+	0.896039i
$962$	−1.66299	+	1.39541i	−0.0536168	+	0.0449899i
$963$		0			0
$964$	−0.878021	−	0.736747i	−0.0282791	−	0.0237290i
$965$	−75.7233	+	38.0296i	−2.43762	+	1.22422i
$966$		0			0
$967$	46.9283	+	5.48513i	1.50911	+	0.176390i	0.830050	−	0.557690i	$-0.188312\pi$
$967$	46.9283	+	5.48513i	1.50911	+	0.176390i	0.679064	+	0.734080i	$0.262386\pi$
$968$	−1.84479	−	31.6738i	−0.0592938	−	1.01804i
$969$		0			0
$970$	16.0700	−	17.0332i	0.515978	−	0.546904i
$971$	40.3149			1.29377			0.646883	−	0.762589i	$-0.276072\pi$
$971$	40.3149			1.29377			0.646883	+	0.762589i	$0.276072\pi$
$972$		0			0
$973$	40.0942			1.28536
$974$	23.6858	−	25.1055i	0.758943	−	0.804432i
$975$		0			0
$976$	−2.04009	−	35.0270i	−0.0653017	−	1.12119i
$977$	2.74591	+	0.320951i	0.0878495	+	0.0102681i	0.159904	−	0.987133i	$-0.448881\pi$
$977$	2.74591	+	0.320951i	0.0878495	+	0.0102681i	−0.0720546	+	0.997401i	$0.522956\pi$
$978$		0			0
$979$	1.69234	−	0.849926i	0.0540875	−	0.0271638i
$980$	−1.64918	−	1.38383i	−0.0526812	−	0.0442048i
$981$		0			0
$982$	31.8360	−	26.7136i	1.01593	−	0.852464i
$983$	0.665653	−	1.54316i	0.0212310	−	0.0492191i	−0.907271	−	0.420547i	$-0.861838\pi$
$983$	0.665653	−	1.54316i	0.0212310	−	0.0492191i	0.928502	+	0.371328i	$0.121097\pi$
$984$		0			0
$985$	38.2335	−	9.06150i	1.21822	−	0.288723i
$986$	−6.28957	+	21.0086i	−0.200301	+	0.669051i
$987$		0			0
$988$	−0.0406744	+	0.00475415i	−0.00129402	+	0.000151250i
$989$	−4.96459	−	28.1556i	−0.157865	−	0.895296i
$990$		0			0
$991$	−1.27536	+	7.23291i	−0.0405130	+	0.229761i	−0.998341	−	0.0575822i	$-0.981661\pi$
$991$	−1.27536	+	7.23291i	−0.0405130	+	0.229761i	0.957828	+	0.287343i	$0.0927720\pi$
$992$	0.0268784	−	0.461484i	0.000853390	−	0.0146521i
$993$		0			0
$994$	3.14151	+	7.28283i	0.0996425	+	0.230997i
$995$	−87.0331	−	43.7097i	−2.75914	−	1.38569i
$996$		0			0
$997$	−18.7413	−	4.44178i	−0.593544	−	0.140673i	−0.0771442	−	0.997020i	$-0.524580\pi$
$997$	−18.7413	−	4.44178i	−0.593544	−	0.140673i	−0.516400	+	0.856347i	$0.672728\pi$
$998$	3.89120	−	6.73976i	0.123174	−	0.213344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.622.3		144
3.2	odd	2		729.2.g.b.622.6		144
9.2	odd	6		729.2.g.a.136.3		144
9.4	even	3		81.2.g.a.43.3	✓	144
9.5	odd	6		243.2.g.a.46.6		144
9.7	even	3		729.2.g.d.136.6		144
81.5	odd	54		243.2.g.a.37.6		144
81.22	even	27	inner	729.2.g.c.109.3		144
81.32	odd	54		729.2.g.a.595.3		144
81.34	even	27		6561.2.a.c.1.54		72
81.47	odd	54		6561.2.a.d.1.19		72
81.49	even	27		729.2.g.d.595.6		144
81.59	odd	54		729.2.g.b.109.6		144
81.76	even	27		81.2.g.a.49.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.43.3	✓	144	9.4	even	3
81.2.g.a.49.3	yes	144	81.76	even	27
243.2.g.a.37.6		144	81.5	odd	54
243.2.g.a.46.6		144	9.5	odd	6
729.2.g.a.136.3		144	9.2	odd	6
729.2.g.a.595.3		144	81.32	odd	54
729.2.g.b.109.6		144	81.59	odd	54
729.2.g.b.622.6		144	3.2	odd	2
729.2.g.c.109.3		144	81.22	even	27	inner
729.2.g.c.622.3		144	1.1	even	1	trivial
729.2.g.d.136.6		144	9.7	even	3
729.2.g.d.595.6		144	81.49	even	27
6561.2.a.c.1.54		72	81.34	even	27
6561.2.a.d.1.19		72	81.47	odd	54

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.947282 + 1.00406i) q^{2} +(0.00549590 + 0.0943610i) q^{4} +(-4.01017 - 0.468722i) q^{5} +(-3.17727 + 1.59569i) q^{7} +(-2.21483 - 1.85846i) q^{8} +O(q^{10})\)	\(q+(-0.947282 + 1.00406i) q^{2} +(0.00549590 + 0.0943610i) q^{4} +(-4.01017 - 0.468722i) q^{5} +(-3.17727 + 1.59569i) q^{7} +(-2.21483 - 1.85846i) q^{8} +(4.26939 - 3.58244i) q^{10} +(0.0643574 - 0.149197i) q^{11} +(0.339729 - 0.0805173i) q^{13} +(1.40761 - 4.70174i) q^{14} +(3.77632 - 0.441388i) q^{16} +(-0.388085 - 2.20094i) q^{17} +(-0.215481 + 1.22205i) q^{19} +(0.0221896 - 0.380980i) q^{20} +(0.0888384 + 0.205951i) q^{22} +(2.70748 + 1.35975i) q^{23} +(10.9966 + 2.60623i) q^{25} +(-0.240975 + 0.417381i) q^{26} +(-0.168033 - 0.291041i) q^{28} +(2.03874 + 6.80987i) q^{29} +(0.722935 - 0.475482i) q^{31} +(0.319024 - 0.428523i) q^{32} +(2.57750 + 1.69525i) q^{34} +(13.4893 - 4.90972i) q^{35} +(4.23271 + 1.54058i) q^{37} +(-1.02289 - 1.37399i) q^{38} +(8.01076 + 8.49090i) q^{40} +(-4.85103 - 5.14179i) q^{41} +(-5.63505 - 7.56918i) q^{43} +(0.0144321 + 0.00525286i) q^{44} +(-3.93001 + 1.43041i) q^{46} +(-3.65368 - 2.40306i) q^{47} +(3.36873 - 4.52499i) q^{49} +(-13.0337 + 8.57237i) q^{50} +(0.00946482 + 0.0316147i) q^{52} +(2.32646 + 4.02955i) q^{53} +(-0.328016 + 0.568141i) q^{55} +(10.0026 + 2.37067i) q^{56} +(-8.76878 - 4.40385i) q^{58} +(2.00630 + 4.65114i) q^{59} +(0.536580 - 9.21273i) q^{61} +(-0.207411 + 1.17629i) q^{62} +(1.44849 + 8.21478i) q^{64} +(-1.40011 + 0.163650i) q^{65} +(3.72757 - 12.4510i) q^{67} +(0.205550 - 0.0487163i) q^{68} +(-7.84856 + 18.1950i) q^{70} +(-1.23797 + 1.03878i) q^{71} +(-8.94621 - 7.50676i) q^{73} +(-5.55640 + 2.79053i) q^{74} +(-0.116499 - 0.0136167i) q^{76} +(0.0335910 + 0.576734i) q^{77} +(4.94986 - 5.24655i) q^{79} -15.3506 q^{80} +9.75795 q^{82} +(1.57700 - 1.67153i) q^{83} +(0.524660 + 9.00806i) q^{85} +(12.9379 + 1.51222i) q^{86} +(-0.419819 + 0.210841i) q^{88} +(8.92827 + 7.49171i) q^{89} +(-0.950932 + 0.797927i) q^{91} +(-0.113427 + 0.262953i) q^{92} +(5.87389 - 1.39214i) q^{94} +(1.43692 - 4.79965i) q^{95} +(4.17332 - 0.487791i) q^{97} +(1.35223 + 7.66885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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