LMFDB - Embedded newform 729.2.g.c.109.3

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			109.3
Character	$\chi$	$=$	729.109
Dual form			729.2.g.c.622.3

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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	0.299952	−	0.953954i	$-0.403029\pi$
$2$	−0.947282	−	1.00406i	−0.669829	−	0.709978i	−0.969781	+	0.243977i	$0.921548\pi$
$3$		0			0
$3$		0			0
$4$	0.00549590	−	0.0943610i	0.00274795	−	0.0471805i
$5$	−4.01017	+	0.468722i	−1.79340	+	0.209619i	−0.946627	−	0.322330i	$-0.895534\pi$
$5$	−4.01017	+	0.468722i	−1.79340	+	0.209619i	−0.846777	+	0.531949i	$0.821460\pi$
$6$		0			0
$7$	−3.17727	−	1.59569i	−1.20090	−	0.603113i	−0.268056	−	0.963403i	$-0.586381\pi$
$7$	−3.17727	−	1.59569i	−1.20090	−	0.603113i	−0.932840	+	0.360291i	$0.882677\pi$
$8$	−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	0.927643	−	0.373469i	$-0.121832\pi$
$11$	0.0643574	+	0.149197i	0.0194045	+	0.0449847i	−0.908238	+	0.418453i	$0.862572\pi$
$12$		0			0
$13$	0.339729	+	0.0805173i	0.0942240	+	0.0223315i	0.277457	−	0.960738i	$-0.410508\pi$
$13$	0.339729	+	0.0805173i	0.0942240	+	0.0223315i	−0.183233	+	0.983069i	$0.558656\pi$
$14$	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	0.900888	+	0.434053i	$0.142917\pi$
$17$	−0.388085	+	2.20094i	−0.0941245	+	0.533807i	−0.995012	+	0.0997542i	$0.968194\pi$
$18$		0			0
$19$	−0.215481	−	1.22205i	−0.0494348	−	0.280358i	0.950063	−	0.312059i	$-0.101019\pi$
$19$	−0.215481	−	1.22205i	−0.0494348	−	0.280358i	−0.999497	+	0.0317008i	$0.989908\pi$
$20$	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	−0.143547	−	0.989643i	$-0.545851\pi$
$23$	2.70748	−	1.35975i	0.564548	−	0.283527i	0.708095	+	0.706117i	$0.249555\pi$
$24$		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	−0.530406	−	0.847744i	$-0.677960\pi$
$29$	2.03874	−	6.80987i	0.378585	−	1.26456i	0.908990	−	0.416817i	$-0.136854\pi$
$30$		0			0
$31$	0.722935	+	0.475482i	0.129843	+	0.0853991i	0.612769	−	0.790262i	$-0.290056\pi$
$31$	0.722935	+	0.475482i	0.129843	+	0.0853991i	−0.482926	+	0.875661i	$0.660426\pi$
$32$	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	0.0302136	−	0.999543i	$-0.490381\pi$
$37$	4.23271	−	1.54058i	0.695853	−	0.253270i	0.665639	+	0.746274i	$0.268159\pi$
$38$	−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	−0.985320	−	0.170715i	$-0.945392\pi$
$41$	−4.85103	+	5.14179i	−0.757603	+	0.803012i	0.227717	+	0.973727i	$0.426874\pi$
$42$		0			0
$43$	−5.63505	+	7.56918i	−0.859336	+	1.15429i	0.127383	+	0.991854i	$0.459342\pi$
$43$	−5.63505	+	7.56918i	−0.859336	+	1.15429i	−0.986719	+	0.162435i	$0.948065\pi$
$44$	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	−0.787283	−	0.616592i	$-0.788513\pi$
$47$	−3.65368	+	2.40306i	−0.532944	+	0.350523i	0.254338	+	0.967115i	$0.418142\pi$
$48$		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	−0.660833	−	0.750533i	$-0.729797\pi$
$53$	2.32646	−	4.02955i	0.319564	−	0.553502i	0.980397	+	0.197031i	$0.0631301\pi$
$54$		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	−0.736266	−	0.676692i	$-0.763413\pi$
$59$	2.00630	−	4.65114i	0.261199	−	0.605526i	0.997464	+	0.0711659i	$0.0226720\pi$
$60$		0			0
$61$	0.536580	+	9.21273i	0.0687021	+	1.17957i	0.839816	+	0.542872i	$0.182663\pi$
$61$	0.536580	+	9.21273i	0.0687021	+	1.17957i	−0.771114	+	0.636698i	$0.780300\pi$
$62$	−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	0.810182	+	0.586179i	$0.199368\pi$
$67$	3.72757	+	12.4510i	0.455395	+	1.52113i	−0.354786	+	0.934947i	$0.615446\pi$
$68$	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	0.566365	−	0.824155i	$-0.308349\pi$
$71$	−1.23797	−	1.03878i	−0.146921	−	0.123281i	−0.713286	+	0.700874i	$0.752794\pi$
$72$		0			0
$73$	−8.94621	+	7.50676i	−1.04707	+	0.878600i	−0.992783	−	0.119925i	$-0.961734\pi$
$73$	−8.94621	+	7.50676i	−1.04707	+	0.878600i	−0.0542914	+	0.998525i	$0.517290\pi$
$74$	−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	0.943255	−	0.332068i	$-0.107746\pi$
$79$	4.94986	+	5.24655i	0.556903	+	0.590283i	−0.386352	+	0.922351i	$0.626265\pi$
$80$	−15.3506			−1.71625
$81$		0			0
$82$	9.75795			1.07759
$83$	1.57700	+	1.67153i	0.173099	+	0.183474i	0.808115	−	0.589025i	$-0.200488\pi$
$83$	1.57700	+	1.67153i	0.173099	+	0.183474i	−0.635016	+	0.772499i	$0.719007\pi$
$84$		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	−0.0322920	−	0.999478i	$-0.510281\pi$
$89$	8.92827	−	7.49171i	0.946395	−	0.794119i	0.978687	+	0.205359i	$0.0658362\pi$
$90$		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	0.325289	−	0.945615i	$-0.394538\pi$
$97$	4.17332	+	0.487791i	0.423736	+	0.0495277i	0.0984472	+	0.995142i	$0.468612\pi$
$98$	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	0.999681	+	0.0252641i	$0.00804267\pi$
$101$	0.0974081	+	1.67243i	0.00969247	+	0.166413i	−0.989988	+	0.141149i	$0.954920\pi$
$102$		0			0
$103$	1.33015	−	3.08363i	0.131064	−	0.303839i	−0.840030	−	0.542541i	$-0.817462\pi$
$103$	1.33015	−	3.08363i	0.131064	−	0.303839i	0.971093	+	0.238701i	$0.0767217\pi$
$104$	−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	0.996491	+	0.0836983i	$0.0266732\pi$
$107$	5.90368	+	10.2255i	0.570730	+	0.988534i	−0.425761	+	0.904836i	$0.639993\pi$
$108$		0			0
$109$	5.03157	−	8.71493i	0.481937	−	0.834739i	−0.517848	−	0.855472i	$-0.673267\pi$
$109$	5.03157	−	8.71493i	0.481937	−	0.834739i	0.999785	+	0.0207336i	$0.00660019\pi$
$110$	−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	0.898103	−	0.439784i	$-0.144945\pi$
$113$	2.33029	+	3.13013i	0.219215	+	0.294457i	−0.678888	+	0.734242i	$0.737538\pi$
$114$		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	−0.0391867	−	0.999232i	$-0.512477\pi$
$127$	−8.01819	−	2.91838i	−0.711499	−	0.258965i	−0.672313	+	0.740267i	$0.734699\pi$
$128$	−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	0.979188	−	0.202958i	$-0.0650554\pi$
$131$	13.5133	+	8.88786i	1.18066	+	0.776536i	0.201477	+	0.979493i	$0.435426\pi$
$132$		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	−0.370243	−	0.928935i	$-0.620726\pi$
$137$	−3.32647	+	0.788388i	−0.284200	+	0.0673566i	0.0860437	+	0.996291i	$0.472578\pi$
$138$		0			0
$139$	−10.0773	+	5.06102i	−0.854747	+	0.429270i	−0.821521	−	0.570178i	$-0.806874\pi$
$139$	−10.0773	+	5.06102i	−0.854747	+	0.429270i	−0.0332254	+	0.999448i	$0.510578\pi$
$140$	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	0.206723	−	0.978399i	$-0.433720\pi$
$149$	−0.581605	−	0.137843i	−0.0476470	−	0.0112925i	−0.254370	+	0.967107i	$0.581868\pi$
$150$		0			0
$151$	0.664309	+	1.54004i	0.0540607	+	0.125327i	0.943106	−	0.332493i	$-0.107890\pi$
$151$	0.664309	+	1.54004i	0.0540607	+	0.125327i	−0.889045	+	0.457820i	$0.848631\pi$
$152$	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	−0.469683	−	0.882835i	$-0.655632\pi$
$157$	−9.06055	+	1.05903i	−0.723110	+	0.0845195i	−0.253427	+	0.967354i	$0.581558\pi$
$158$	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	0.0864616	−	0.996255i	$-0.472444\pi$
$167$	5.17360	−	0.604707i	0.400345	−	0.0467936i	0.313883	+	0.949462i	$0.398370\pi$
$168$		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	0.873493	+	0.486837i	$0.161849\pi$
$173$	8.26239	+	19.1544i	0.628178	+	1.45628i	−0.245315	+	0.969444i	$0.578891\pi$
$174$		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	−0.999772	−	0.0213413i	$-0.993206\pi$
$179$	−0.709018	+	4.02104i	−0.0529945	+	0.300547i	0.946778	+	0.321888i	$0.104317\pi$
$180$		0			0
$181$	2.85517	+	16.1925i	0.212223	+	1.20358i	0.885661	+	0.464333i	$0.153706\pi$
$181$	2.85517	+	16.1925i	0.212223	+	1.20358i	−0.673437	+	0.739244i	$0.735183\pi$
$182$	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	−0.957946	−	0.286948i	$-0.907359\pi$
$191$	0.00119573	−	0.00399401i	8.65198e−5	−	0.000288996i	0.958033	+	0.286659i	$0.0925446\pi$
$192$		0			0
$193$	17.5348	+	11.5328i	1.26218	+	0.830150i	0.991192	−	0.132432i	$-0.0422785\pi$
$193$	17.5348	+	11.5328i	1.26218	+	0.830150i	0.270990	+	0.962582i	$0.412649\pi$
$194$	−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	−0.00497138	−	0.999988i	$-0.501582\pi$
$197$	−9.14507	−	3.32853i	−0.651559	−	0.237148i	−0.646588	+	0.762839i	$0.723805\pi$
$198$		0			0
$199$	22.6674	−	8.25026i	1.60685	−	0.584846i	0.626036	−	0.779794i	$-0.284676\pi$
$199$	22.6674	−	8.25026i	1.60685	−	0.584846i	0.980814	+	0.194948i	$0.0624539\pi$
$200$	−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	0.995444	−	0.0953471i	$-0.0303961\pi$
$211$	8.98577	+	12.0700i	0.618606	+	0.830932i	−0.376838	+	0.926279i	$0.622989\pi$
$212$	−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	−0.964719	−	0.263283i	$-0.915195\pi$
$223$	−0.553847	−	9.50919i	−0.0370883	−	0.636782i	0.927630	−	0.373500i	$-0.121842\pi$
$224$	−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	−0.297709	−	0.954657i	$-0.596223\pi$
$227$	−12.1670	−	1.42212i	−0.807553	−	0.0943894i	−0.509843	+	0.860267i	$0.670297\pi$
$228$		0			0
$229$	−1.07081	−	3.57674i	−0.0707608	−	0.236358i	0.915292	−	0.402791i	$-0.131960\pi$
$229$	−1.07081	−	3.57674i	−0.0707608	−	0.236358i	−0.986053	+	0.166434i	$0.946775\pi$
$230$	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	0.990727	−	0.135865i	$-0.0433813\pi$
$233$	15.7065	+	13.1793i	1.02896	+	0.863404i	0.0382373	+	0.999269i	$0.487826\pi$
$234$		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	−0.882139	−	0.470989i	$-0.843897\pi$
$239$	0.753096	−	12.9302i	0.0487137	−	0.836382i	0.930853	−	0.365394i	$-0.119066\pi$
$240$		0			0
$241$	−8.32147	−	8.82024i	−0.536033	−	0.568162i	0.401588	−	0.915820i	$-0.368458\pi$
$241$	−8.32147	−	8.82024i	−0.536033	−	0.568162i	−0.937621	+	0.347659i	$0.886977\pi$
$242$	−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	−0.400705	+	0.916207i	$0.631235\pi$
$251$	−21.7457	+	18.2468i	−1.37257	+	1.15173i	−0.971869	+	0.235520i	$0.924321\pi$
$252$		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	−0.739031	−	0.673672i	$-0.764716\pi$
$257$	−7.88365	−	26.3332i	−0.491768	−	1.64262i	0.247262	−	0.968949i	$-0.420469\pi$
$258$		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	−0.996348	−	0.0853856i	$-0.972788\pi$
$263$	−0.270011	−	4.63592i	−0.0166496	−	0.285863i	0.979698	−	0.200477i	$-0.0642493\pi$
$264$		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	0.932291	−	0.361709i	$-0.117807\pi$
$269$	2.50768	+	4.34343i	0.152896	+	0.264824i	−0.779395	+	0.626533i	$0.784473\pi$
$270$		0			0
$271$	−8.04356	+	13.9319i	−0.488612	+	0.846300i	−0.999914	−	0.0131007i	$-0.995830\pi$
$271$	−8.04356	+	13.9319i	−0.488612	+	0.846300i	0.511303	+	0.859401i	$0.329163\pi$
$272$	−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	−0.771956	−	0.635676i	$-0.780721\pi$
$277$	−8.22220	+	5.40783i	−0.494024	+	0.324925i	0.277932	+	0.960601i	$0.410351\pi$
$278$	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	−0.223307	−	0.974748i	$-0.571685\pi$
$281$	12.9836	−	17.4400i	0.774537	−	1.04038i	0.997844	−	0.0656355i	$-0.0209075\pi$
$282$		0			0
$283$	3.29612	−	3.49368i	0.195934	−	0.207678i	−0.621956	−	0.783052i	$-0.713662\pi$
$283$	3.29612	−	3.49368i	0.195934	−	0.207678i	0.817891	+	0.575374i	$0.195143\pi$
$284$	−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	0.679862	−	0.733340i	$-0.262040\pi$
$293$	4.72054	+	3.10475i	0.275777	+	0.181381i	−0.404085	+	0.914721i	$0.632410\pi$
$294$		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	−0.919358	−	0.393421i	$-0.871291\pi$
$307$	1.38619	−	7.86146i	0.0791139	−	0.448677i	0.998472	−	0.0552559i	$-0.0175975\pi$
$308$	−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	−0.382569	−	0.923927i	$-0.624961\pi$
$311$	−20.0883	−	4.76101i	−1.13910	−	0.269972i	−0.756534	+	0.653955i	$0.773109\pi$
$312$		0			0
$313$	7.69699	+	17.8436i	0.435060	+	1.00858i	0.984870	+	0.173293i	$0.0554407\pi$
$313$	7.69699	+	17.8436i	0.435060	+	1.00858i	−0.549811	+	0.835289i	$0.685300\pi$
$314$	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	0.988850	−	0.148918i	$-0.0475789\pi$
$317$	25.9928	+	13.0541i	1.45990	+	0.733189i	0.471050	+	0.882107i	$0.343875\pi$
$318$		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	0.522624	−	0.852563i	$-0.324953\pi$
$331$	2.74452	+	1.37835i	0.150853	+	0.0757611i	−0.371771	+	0.928324i	$0.621249\pi$
$332$	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	0.887452	−	0.460900i	$-0.152473\pi$
$337$	27.0527	+	6.41162i	1.47366	+	0.349263i	0.586205	+	0.810163i	$0.300621\pi$
$338$	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	−0.530869	−	0.847454i	$-0.678135\pi$
$347$	−3.13174	+	1.57282i	−0.168120	+	0.0844332i	0.362749	+	0.931887i	$0.381838\pi$
$348$		0			0
$349$	−11.1318	+	2.63829i	−0.595874	+	0.141225i	−0.517476	−	0.855698i	$-0.673128\pi$
$349$	−11.1318	+	2.63829i	−0.595874	+	0.141225i	−0.0783974	+	0.996922i	$0.524980\pi$
$350$	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	−0.942845	−	0.333233i	$-0.891861\pi$
$353$	0.526163	−	1.75751i	0.0280048	−	0.0935426i	0.970849	+	0.239690i	$0.0770458\pi$
$354$		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	0.788673	−	0.614814i	$-0.210769\pi$
$359$	18.9025	+	6.87995i	0.997636	+	0.363110i	0.208964	+	0.977923i	$0.432991\pi$
$360$		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	−0.169487	−	0.985532i	$-0.554211\pi$
$367$	15.7712	−	21.1845i	0.823252	−	1.10582i	0.992739	−	0.120287i	$-0.0383816\pi$
$368$	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	−0.972586	−	0.232544i	$-0.925295\pi$
$373$	−17.6990	−	23.7739i	−0.916420	−	1.23097i	0.0561660	−	0.998421i	$-0.482112\pi$
$374$	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	0.975103	−	0.221753i	$-0.0711778\pi$
$379$	5.75292	+	9.96436i	0.295508	+	0.511835i	−0.679595	+	0.733587i	$0.737844\pi$
$380$	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	0.331649	+	0.943403i	$0.392395\pi$
$383$	−11.3929	+	26.4116i	−0.582149	+	1.34957i	−0.913798	+	0.406169i	$0.866864\pi$
$384$		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	0.399530	−	0.916720i	$-0.369173\pi$
$389$	11.3779	+	1.32988i	0.576881	+	0.0674277i	0.177351	+	0.984148i	$0.443247\pi$
$390$		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	−0.407742	−	0.913097i	$-0.633684\pi$
$397$	8.38197	−	7.03331i	0.420679	−	0.352992i	0.828421	+	0.560105i	$0.189239\pi$
$398$	−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	−0.998775	−	0.0494790i	$-0.984244\pi$
$401$	−0.0202092	+	0.346979i	−0.00100920	+	0.0173273i	0.997766	+	0.0668063i	$0.0212810\pi$
$402$		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	0.713783	+	0.700367i	$0.246980\pi$
$409$	−1.54674	+	26.5565i	−0.0764813	+	1.31313i	−0.790264	+	0.612766i	$0.790057\pi$
$410$	−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	−0.999639	−	0.0268761i	$-0.991444\pi$
$419$	−3.66857	−	12.2539i	−0.179221	−	0.598641i	0.820417	−	0.571765i	$-0.193741\pi$
$420$		0			0
$421$	10.8013	+	1.26249i	0.526424	+	0.0615302i	0.375154	−	0.926962i	$-0.377590\pi$
$421$	10.8013	+	1.26249i	0.526424	+	0.0615302i	0.151270	+	0.988493i	$0.451664\pi$
$422$	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	0.894121	−	0.447825i	$-0.147801\pi$
$431$	1.22970	+	2.12989i	0.0592323	+	0.102593i	−0.834889	+	0.550419i	$0.814468\pi$
$432$		0			0
$433$	6.44336	−	11.1602i	0.309648	−	0.536326i	−0.668637	−	0.743589i	$-0.733122\pi$
$433$	6.44336	−	11.1602i	0.309648	−	0.536326i	0.978285	+	0.207263i	$0.0664554\pi$
$434$	−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	0.135746	−	0.990744i	$-0.456657\pi$
$439$	23.0314	−	15.1480i	1.09923	−	0.722975i	0.963483	+	0.267769i	$0.0862864\pi$
$440$	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	−0.713311	−	0.700848i	$-0.752805\pi$
$443$	3.42388	−	4.59907i	0.162673	−	0.218508i	0.875985	+	0.482339i	$0.160213\pi$
$444$		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	−0.962852	−	0.270030i	$-0.912966\pi$
$449$	−32.3537	+	11.7758i	−1.52687	+	0.555734i	−0.564015	+	0.825764i	$0.690744\pi$
$450$		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	−0.891890	−	0.452252i	$-0.850621\pi$
$457$	2.17602	−	7.26841i	0.101790	−	0.340002i	0.993680	+	0.112250i	$0.0358059\pi$
$458$	−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	−0.272124	−	0.962262i	$-0.587726\pi$
$461$	−1.79155	+	0.424604i	−0.0834406	+	0.0197758i	0.188683	+	0.982038i	$0.439578\pi$
$462$		0			0
$463$	−20.1099	+	10.0996i	−0.934588	+	0.469368i	−0.849844	−	0.527035i	$-0.823304\pi$
$463$	−20.1099	+	10.0996i	−0.934588	+	0.469368i	−0.0847444	+	0.996403i	$0.527007\pi$
$464$	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	0.562071	+	0.827089i	$0.310005\pi$
$467$	6.84563	+	38.8235i	0.316778	+	1.79654i	−0.245292	+	0.969449i	$0.578884\pi$
$468$		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	0.394100	−	0.919068i	$-0.371056\pi$
$479$	−2.35856	−	1.18451i	−0.107765	−	0.0541217i	−0.501865	+	0.864946i	$0.667353\pi$
$480$		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	−0.759944	−	0.649988i	$-0.774774\pi$
$491$	−29.9031	+	3.49517i	−1.34951	+	0.157735i	−0.589563	+	0.807723i	$0.700700\pi$
$492$		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	0.105982	−	0.994368i	$-0.466201\pi$
$499$	−5.48586	−	1.30017i	−0.245581	−	0.0582037i	−0.351563	+	0.936164i	$0.614350\pi$
$500$	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	−0.906595	−	0.422002i	$-0.861328\pi$
$503$	2.01083	−	11.4040i	0.0896587	−	0.508479i	0.996254	−	0.0864779i	$-0.0275612\pi$
$504$		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	0.437899	−	0.899024i	$-0.355723\pi$
$509$	32.0484	−	16.0953i	1.42052	−	0.713413i	0.982623	+	0.185611i	$0.0594265\pi$
$510$		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	0.518761	−	0.854919i	$-0.326393\pi$
$521$	8.36834	+	3.04583i	0.366624	+	0.133440i	−0.152137	+	0.988359i	$0.548616\pi$
$522$		0			0
$523$	−15.1809	+	5.52540i	−0.663815	+	0.241609i	−0.651883	−	0.758320i	$-0.726021\pi$
$523$	−15.1809	+	5.52540i	−0.663815	+	0.241609i	−0.0119324	+	0.999929i	$0.503798\pi$
$524$	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	0.949919	−	0.312497i	$-0.101165\pi$
$541$	4.75257	+	8.23170i	0.204329	+	0.353908i	−0.745590	+	0.666405i	$0.767832\pi$
$542$	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	−0.998460	−	0.0554726i	$-0.982333\pi$
$547$	−0.308516	−	5.29702i	−0.0131912	−	0.226484i	0.985269	−	0.171012i	$-0.0547036\pi$
$548$	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	0.994795	−	0.101895i	$-0.0324904\pi$
$557$	25.1867	+	21.1341i	1.06719	+	0.895481i	0.0723978	+	0.997376i	$0.476935\pi$
$558$		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	0.945857	+	0.324583i	$0.105224\pi$
$563$	−0.742347	+	12.7456i	−0.0312862	+	0.537163i	−0.977144	+	0.212581i	$0.931813\pi$
$564$		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	0.933979	+	0.357329i	$0.116313\pi$
$569$	29.4927	+	31.2604i	1.23640	+	1.31050i	0.302419	+	0.953175i	$0.402206\pi$
$570$		0			0
$571$	0.221256	−	3.79881i	0.00925926	−	0.158975i	−0.990509	−	0.137448i	$-0.956110\pi$
$571$	0.221256	−	3.79881i	0.00925926	−	0.158975i	0.999768	−	0.0215274i	$-0.00685292\pi$
$572$	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	0.850443	−	0.526067i	$-0.176334\pi$
$577$	11.5311	+	9.67573i	0.480045	+	0.402806i	−0.370397	+	0.928873i	$0.620779\pi$
$578$	−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	0.661822	+	0.749661i	$0.269784\pi$
$587$	2.21700	+	38.0644i	0.0915054	+	1.57109i	−0.570316	+	0.821425i	$0.693179\pi$
$588$		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	0.960354	−	0.278785i	$-0.0899317\pi$
$593$	5.81375	+	10.0697i	0.238742	+	0.413513i	−0.721612	+	0.692298i	$0.756598\pi$
$594$		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	−0.946046	−	0.324032i	$-0.894961\pi$
$599$	−24.1107	−	32.3863i	−0.985136	−	1.32327i	−0.0390903	−	0.999236i	$-0.512446\pi$
$600$		0			0
$601$	16.4724	−	10.8341i	0.671925	−	0.441932i	−0.167162	−	0.985929i	$-0.553460\pi$
$601$	16.4724	−	10.8341i	0.671925	−	0.441932i	0.839087	+	0.543998i	$0.183090\pi$
$602$	−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	−0.752477	−	0.658618i	$-0.771141\pi$
$607$	−1.26194	+	1.33758i	−0.0512205	+	0.0542906i	0.701257	+	0.712909i	$0.252623\pi$
$608$	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	−0.433379	−	0.901212i	$-0.642679\pi$
$613$	−33.2921	−	12.1173i	−1.34465	−	0.489414i	−0.911275	+	0.411797i	$0.864901\pi$
$614$	−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	0.989476	−	0.144700i	$-0.0462217\pi$
$617$	31.0126	+	20.3973i	1.24852	+	0.821165i	0.259045	+	0.965865i	$0.416592\pi$
$618$		0			0
$619$	−9.74402	+	32.5473i	−0.391645	+	1.30819i	0.504110	+	0.863639i	$0.331821\pi$
$619$	−9.74402	+	32.5473i	−0.391645	+	1.30819i	−0.895755	+	0.444547i	$0.853365\pi$
$620$	−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	0.922493	+	0.386013i	$0.126148\pi$
$631$	−1.91892	+	10.8828i	−0.0763912	+	0.433236i	−0.998884	+	0.0472226i	$0.984963\pi$
$632$	−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	0.712017	−	0.702162i	$-0.247782\pi$
$641$	14.5321	+	7.29830i	0.573984	+	0.288265i	−0.138033	+	0.990428i	$0.544078\pi$
$642$		0			0
$643$	−14.1768	+	1.65703i	−0.559078	+	0.0653468i	−0.390939	−	0.920416i	$-0.627850\pi$
$643$	−14.1768	+	1.65703i	−0.559078	+	0.0653468i	−0.168139	+	0.985763i	$0.553776\pi$
$644$	−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	−0.165961	−	0.986132i	$-0.553072\pi$
$653$	−2.55616	+	0.298772i	−0.100030	+	0.0116918i	0.0659306	+	0.997824i	$0.478998\pi$
$654$		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	0.839054	−	0.544048i	$-0.183109\pi$
$659$	−3.40053	−	7.88331i	−0.132466	−	0.307090i	−0.971520	+	0.236958i	$0.923850\pi$
$660$		0			0
$661$	36.0921	+	8.55398i	1.40382	+	0.332711i	0.861626	−	0.507543i	$-0.169446\pi$
$661$	36.0921	+	8.55398i	1.40382	+	0.332711i	0.542192	+	0.840254i	$0.317594\pi$
$662$	−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	0.207492	−	0.978237i	$-0.433470\pi$
$673$	21.5825	−	5.11516i	0.831946	−	0.197175i	0.624454	+	0.781062i	$0.285322\pi$
$674$	−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	−0.978539	−	0.206064i	$-0.933935\pi$
$677$	−1.24236	+	4.14976i	−0.0477477	+	0.159488i	0.930791	+	0.365552i	$0.119120\pi$
$678$		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	−0.511077	−	0.859535i	$-0.670753\pi$
$683$	−38.0275	−	13.8409i	−1.45508	−	0.529607i	−0.944006	+	0.329928i	$0.892976\pi$
$684$		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	−0.983740	−	0.179598i	$-0.942520\pi$
$691$	−13.9201	+	18.6980i	−0.529547	+	0.711305i	0.454193	+	0.890903i	$0.349928\pi$
$692$	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	−0.956532	−	0.291627i	$-0.905804\pi$
$701$	−5.97599	+	10.3507i	−0.225710	+	0.390941i	0.730822	+	0.682568i	$0.239137\pi$
$702$		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	0.977288	+	0.211918i	$0.0679708\pi$
$709$	0.831035	+	14.2683i	0.0312102	+	0.535858i	−0.946077	+	0.323941i	$0.894992\pi$
$710$	−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	0.432004	−	0.901872i	$-0.357807\pi$
$719$	−10.2202	−	8.57578i	−0.381150	−	0.319823i	−0.813154	+	0.582049i	$0.802251\pi$
$720$		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	−0.993515	−	0.113698i	$-0.963730\pi$
$727$	−28.2910	−	29.9867i	−1.04925	−	1.11214i	−0.0557382	−	0.998445i	$-0.517751\pi$
$728$	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	0.962617	+	0.270868i	$0.0873106\pi$
$733$	−0.675142	+	11.5917i	−0.0249369	+	0.428151i	−0.987554	+	0.157283i	$0.949726\pi$
$734$	−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	−0.0300588	−	0.999548i	$-0.509569\pi$
$739$	−27.7185	−	23.2586i	−1.01964	−	0.855581i	−0.989582	+	0.143968i	$0.954014\pi$
$740$	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	0.623352	+	0.781941i	$0.285770\pi$
$743$	14.5076	+	48.4588i	0.532233	+	1.77778i	−0.0911193	+	0.995840i	$0.529044\pi$
$744$		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	−0.329599	−	0.944121i	$-0.606914\pi$
$751$	15.9854	−	37.0582i	0.583314	−	1.35227i	0.912913	−	0.408154i	$-0.133827\pi$
$752$	−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	−0.0405607	−	0.999177i	$-0.512914\pi$
$757$	23.2499	−	40.2700i	0.845032	−	1.46364i	0.885593	−	0.464462i	$-0.153752\pi$
$758$	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	0.723295	−	0.690539i	$-0.242627\pi$
$761$	−4.01868	−	5.39803i	−0.145677	−	0.195678i	−0.868972	+	0.494860i	$0.835219\pi$
$762$		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	−0.965257	−	0.261302i	$-0.915848\pi$
$769$	−17.9772	+	19.0547i	−0.648273	+	0.687129i	0.316984	+	0.948431i	$0.397330\pi$
$770$	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	−0.0470079	−	0.998895i	$-0.514969\pi$
$773$	15.5434	−	5.65735i	0.559059	−	0.203481i	0.606067	+	0.795414i	$0.292746\pi$
$774$		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

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

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