LMFDB - Embedded newform 729.2.g.a.28.7

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			28.7
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68031 - 1.10516i) q^{2} +(0.809915 - 1.87759i) q^{4} +(-2.40279 + 2.54681i) q^{5} +(-2.90760 - 0.339850i) q^{7} +(-0.0156557 - 0.0887876i) q^{8} +O(q^{10})$	\(q+(1.68031 - 1.10516i) q^{2} +(0.809915 - 1.87759i) q^{4} +(-2.40279 + 2.54681i) q^{5} +(-2.90760 - 0.339850i) q^{7} +(-0.0156557 - 0.0887876i) q^{8} +(-1.22281 + 6.93490i) q^{10} +(-0.442621 + 1.47846i) q^{11} +(-0.123669 + 2.12332i) q^{13} +(-5.26127 + 2.64231i) q^{14} +(2.68206 + 2.84282i) q^{16} +(-4.47367 + 1.62828i) q^{17} +(-5.79274 - 2.10839i) q^{19} +(2.83582 + 6.57416i) q^{20} +(0.890189 + 2.97344i) q^{22} +(1.94108 - 0.226880i) q^{23} +(-0.422110 - 7.24736i) q^{25} +(2.13880 + 3.70451i) q^{26} +(-2.99301 + 5.18405i) q^{28} +(5.17918 + 2.60108i) q^{29} +(-0.550579 - 0.739556i) q^{31} +(7.82392 + 1.85430i) q^{32} +(-5.71766 + 7.68015i) q^{34} +(7.85190 - 6.58853i) q^{35} +(2.61187 + 2.19162i) q^{37} +(-12.0637 + 2.85915i) q^{38} +(0.263742 + 0.173466i) q^{40} +(7.40100 + 4.86772i) q^{41} +(-4.29716 + 1.01845i) q^{43} +(2.41746 + 2.02849i) q^{44} +(3.01089 - 2.52643i) q^{46} +(3.76326 - 5.05493i) q^{47} +(1.52735 + 0.361989i) q^{49} +(-8.71876 - 11.7113i) q^{50} +(3.88657 + 1.95191i) q^{52} +(-4.19943 + 7.27362i) q^{53} +(-2.70182 - 4.67970i) q^{55} +(0.0153460 + 0.263480i) q^{56} +(11.5772 - 1.35319i) q^{58} +(0.648147 + 2.16496i) q^{59} +(-5.46905 - 12.6787i) q^{61} +(-1.74247 - 0.634208i) q^{62} +(7.85068 - 2.85741i) q^{64} +(-5.11053 - 5.41685i) q^{65} +(1.80329 - 0.905649i) q^{67} +(-0.566039 + 9.71852i) q^{68} +(5.91228 - 19.7484i) q^{70} +(0.0422183 - 0.239432i) q^{71} +(-0.806129 - 4.57178i) q^{73} +(6.81086 + 0.796075i) q^{74} +(-8.65032 + 9.16881i) q^{76} +(1.78942 - 4.14835i) q^{77} +(2.65633 - 1.74709i) q^{79} -13.6846 q^{80} +17.8156 q^{82} +(-12.3106 + 8.09679i) q^{83} +(6.60237 - 15.3060i) q^{85} +(-6.09503 + 6.46036i) q^{86} +(0.138198 + 0.0161531i) q^{88} +(1.80000 + 10.2083i) q^{89} +(1.08119 - 6.13174i) q^{91} +(1.14612 - 3.82832i) q^{92} +(0.736946 - 12.6529i) q^{94} +(19.2884 - 9.68700i) q^{95} +(9.08709 + 9.63176i) q^{97} +(2.96649 - 1.07971i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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 $

$2$	1.68031	−	1.10516i	1.18816	−	0.781466i	0.207702	−	0.978192i	$-0.433401\pi$
$2$	1.68031	−	1.10516i	1.18816	−	0.781466i	0.980458	+	0.196727i	$0.0630311\pi$
$3$		0			0
$3$		0			0
$4$	0.809915	−	1.87759i	0.404958	−	0.938797i
$5$	−2.40279	+	2.54681i	−1.07456	+	1.13897i	−0.0847755	+	0.996400i	$0.527017\pi$
$5$	−2.40279	+	2.54681i	−1.07456	+	1.13897i	−0.989785	+	0.142568i	$0.954464\pi$
$6$		0			0
$7$	−2.90760	−	0.339850i	−1.09897	−	0.128451i	−0.452777	−	0.891624i	$-0.649567\pi$
$7$	−2.90760	−	0.339850i	−1.09897	−	0.128451i	−0.646195	+	0.763173i	$0.723641\pi$
$8$	−0.0156557	−	0.0887876i	−0.00553511	−	0.0313912i
$9$		0			0
$10$	−1.22281	+	6.93490i	−0.386687	+	2.19301i
$11$	−0.442621	+	1.47846i	−0.133455	+	0.445772i	−0.998428	−	0.0560469i	$-0.982150\pi$
$11$	−0.442621	+	1.47846i	−0.133455	+	0.445772i	0.864973	+	0.501819i	$0.167336\pi$
$12$		0			0
$13$	−0.123669	+	2.12332i	−0.0342997	+	0.588902i	0.936746	+	0.350009i	$0.113822\pi$
$13$	−0.123669	+	2.12332i	−0.0342997	+	0.588902i	−0.971046	+	0.238893i	$0.923215\pi$
$14$	−5.26127	+	2.64231i	−1.40613	+	0.706187i
$15$		0			0
$16$	2.68206	+	2.84282i	0.670515	+	0.710705i
$17$	−4.47367	+	1.62828i	−1.08503	+	0.394917i	−0.821776	−	0.569811i	$-0.807016\pi$
$17$	−4.47367	+	1.62828i	−1.08503	+	0.394917i	−0.263250	+	0.964728i	$0.584794\pi$
$18$		0			0
$19$	−5.79274	−	2.10839i	−1.32895	−	0.483697i	−0.422632	−	0.906301i	$-0.638894\pi$
$19$	−5.79274	−	2.10839i	−1.32895	−	0.483697i	−0.906314	+	0.422604i	$0.861116\pi$
$20$	2.83582	+	6.57416i	0.634108	+	1.47003i
$21$		0			0
$22$	0.890189	+	2.97344i	0.189789	+	0.633939i
$23$	1.94108	−	0.226880i	0.404743	−	0.0473077i	0.0887141	−	0.996057i	$-0.471724\pi$
$23$	1.94108	−	0.226880i	0.404743	−	0.0473077i	0.316029	+	0.948749i	$0.397650\pi$
$24$		0			0
$25$	−0.422110	−	7.24736i	−0.0844221	−	1.44947i
$26$	2.13880	+	3.70451i	0.419453	+	0.726515i
$27$		0			0
$28$	−2.99301	+	5.18405i	−0.565626	+	0.979694i
$29$	5.17918	+	2.60108i	0.961749	+	0.483009i	0.859155	−	0.511715i	$-0.170990\pi$
$29$	5.17918	+	2.60108i	0.961749	+	0.483009i	0.102594	+	0.994723i	$0.467286\pi$
$30$		0			0
$31$	−0.550579	−	0.739556i	−0.0988869	−	0.132828i	0.749926	−	0.661522i	$-0.230089\pi$
$31$	−0.550579	−	0.739556i	−0.0988869	−	0.132828i	−0.848812	+	0.528694i	$0.822682\pi$
$32$	7.82392	+	1.85430i	1.38309	+	0.327798i
$33$		0			0
$34$	−5.71766	+	7.68015i	−0.980571	+	1.31713i
$35$	7.85190	−	6.58853i	1.32721	−	1.11366i
$36$		0			0
$37$	2.61187	+	2.19162i	0.429390	+	0.360301i	0.831721	−	0.555193i	$-0.187356\pi$
$37$	2.61187	+	2.19162i	0.429390	+	0.360301i	−0.402332	+	0.915494i	$0.631800\pi$
$38$	−12.0637	+	2.85915i	−1.95699	+	0.463816i
$39$		0			0
$40$	0.263742	+	0.173466i	0.0417013	+	0.0274274i
$41$	7.40100	+	4.86772i	1.15584	+	0.760210i	0.974759	−	0.223258i	$-0.0716692\pi$
$41$	7.40100	+	4.86772i	1.15584	+	0.760210i	0.181083	+	0.983468i	$0.442040\pi$
$42$		0			0
$43$	−4.29716	+	1.01845i	−0.655311	+	0.155312i	−0.544804	−	0.838564i	$-0.683396\pi$
$43$	−4.29716	+	1.01845i	−0.655311	+	0.155312i	−0.110508	+	0.993875i	$0.535248\pi$
$44$	2.41746	+	2.02849i	0.364446	+	0.305806i
$45$		0			0
$46$	3.01089	−	2.52643i	0.443931	−	0.372502i
$47$	3.76326	−	5.05493i	0.548928	−	0.737338i	−0.437916	−	0.899016i	$-0.644283\pi$
$47$	3.76326	−	5.05493i	0.548928	−	0.737338i	0.986844	+	0.161678i	$0.0516906\pi$
$48$		0			0
$49$	1.52735	+	0.361989i	0.218193	+	0.0517128i
$50$	−8.71876	−	11.7113i	−1.23302	−	1.65623i
$51$		0			0
$52$	3.88657	+	1.95191i	0.538970	+	0.270681i
$53$	−4.19943	+	7.27362i	−0.576836	+	0.999109i	0.419004	+	0.907985i	$0.362379\pi$
$53$	−4.19943	+	7.27362i	−0.576836	+	0.999109i	−0.995840	+	0.0911246i	$0.970954\pi$
$54$		0			0
$55$	−2.70182	−	4.67970i	−0.364314	−	0.631010i
$56$	0.0153460	+	0.263480i	0.00205069	+	0.0352090i
$57$		0			0
$58$	11.5772	−	1.35319i	1.52017	−	0.177682i
$59$	0.648147	+	2.16496i	0.0843815	+	0.281854i	0.989758	−	0.142756i	$-0.0455964\pi$
$59$	0.648147	+	2.16496i	0.0843815	+	0.281854i	−0.905376	+	0.424610i	$0.860411\pi$
$60$		0			0
$61$	−5.46905	−	12.6787i	−0.700240	−	1.62334i	−0.779437	−	0.626480i	$-0.784495\pi$
$61$	−5.46905	−	12.6787i	−0.700240	−	1.62334i	0.0791973	−	0.996859i	$-0.474764\pi$
$62$	−1.74247	−	0.634208i	−0.221294	−	0.0805445i
$63$		0			0
$64$	7.85068	−	2.85741i	0.981335	−	0.357177i
$65$	−5.11053	−	5.41685i	−0.633884	−	0.671877i
$66$		0			0
$67$	1.80329	−	0.905649i	0.220308	−	0.110643i	−0.335223	−	0.942139i	$-0.608812\pi$
$67$	1.80329	−	0.905649i	0.220308	−	0.110643i	0.555530	+	0.831496i	$0.312515\pi$
$68$	−0.566039	+	9.71852i	−0.0686423	+	1.17854i
$69$		0			0
$70$	5.91228	−	19.7484i	0.706652	−	2.36038i
$71$	0.0422183	−	0.239432i	0.00501039	−	0.0284154i	−0.982200	−	0.187838i	$-0.939852\pi$
$71$	0.0422183	−	0.239432i	0.00501039	−	0.0284154i	0.987210	+	0.159422i	$0.0509632\pi$
$72$		0			0
$73$	−0.806129	−	4.57178i	−0.0943503	−	0.535087i	−0.994945	−	0.100426i	$-0.967979\pi$
$73$	−0.806129	−	4.57178i	−0.0943503	−	0.535087i	0.900594	−	0.434661i	$-0.143132\pi$
$74$	6.81086	+	0.796075i	0.791746	+	0.0925419i
$75$		0			0
$76$	−8.65032	+	9.16881i	−0.992260	+	1.05173i
$77$	1.78942	−	4.14835i	0.203924	−	0.472748i
$78$		0			0
$79$	2.65633	−	1.74709i	0.298860	−	0.196563i	−0.391218	−	0.920298i	$-0.627946\pi$
$79$	2.65633	−	1.74709i	0.298860	−	0.196563i	0.690079	+	0.723734i	$0.257576\pi$
$80$	−13.6846			−1.52998
$81$		0			0
$82$	17.8156			1.96740
$83$	−12.3106	+	8.09679i	−1.35126	+	0.888738i	−0.998889	−	0.0471222i	$-0.984995\pi$
$83$	−12.3106	+	8.09679i	−1.35126	+	0.888738i	−0.352371	+	0.935860i	$0.614625\pi$
$84$		0			0
$85$	6.60237	−	15.3060i	0.716128	−	1.66017i
$86$	−6.09503	+	6.46036i	−0.657244	+	0.696638i
$87$		0			0
$88$	0.138198	+	0.0161531i	0.0147320	+	0.00172192i
$89$	1.80000	+	10.2083i	0.190799	+	1.08208i	0.918275	+	0.395943i	$0.129582\pi$
$89$	1.80000	+	10.2083i	0.190799	+	1.08208i	−0.727476	+	0.686133i	$0.759307\pi$
$90$		0			0
$91$	1.08119	−	6.13174i	0.113340	−	0.642781i
$92$	1.14612	−	3.82832i	0.119492	−	0.399130i
$93$		0			0
$94$	0.736946	−	12.6529i	0.0760102	−	1.30504i
$95$	19.2884	−	9.68700i	1.97895	−	0.993865i
$96$		0			0
$97$	9.08709	+	9.63176i	0.922654	+	0.977957i	0.999818	−	0.0190619i	$-0.00606795\pi$
$97$	9.08709	+	9.63176i	0.922654	+	0.977957i	−0.0771639	+	0.997018i	$0.524586\pi$
$98$	2.96649	−	1.07971i	0.299660	−	0.109067i
$99$		0			0
$100$	−13.9495	−	5.07719i	−1.39495	−	0.507719i
$101$	−1.67365	−	3.87995i	−0.166534	−	0.386069i	0.814429	−	0.580263i	$-0.197050\pi$
$101$	−1.67365	−	3.87995i	−0.166534	−	0.386069i	−0.980963	+	0.194194i	$0.937791\pi$
$102$		0			0
$103$	1.69805	+	5.67189i	0.167314	+	0.558868i	0.999987	+	0.00510259i	$0.00162421\pi$
$103$	1.69805	+	5.67189i	0.167314	+	0.558868i	−0.832673	+	0.553765i	$0.813191\pi$
$104$	0.190460	−	0.0222616i	0.0186762	−	0.00218293i
$105$		0			0
$106$	0.982158	+	16.8630i	0.0953956	+	1.63788i
$107$	−0.413315	−	0.715883i	−0.0399567	−	0.0692070i	0.845355	−	0.534204i	$-0.179389\pi$
$107$	−0.413315	−	0.715883i	−0.0399567	−	0.0692070i	−0.885312	+	0.464997i	$0.846055\pi$
$108$		0			0
$109$	−5.03364	+	8.71853i	−0.482136	+	0.835083i	−0.999790	−	0.0205067i	$-0.993472\pi$
$109$	−5.03364	+	8.71853i	−0.482136	+	0.835083i	0.517654	+	0.855590i	$0.326805\pi$
$110$	−9.71172	−	4.87741i	−0.925976	−	0.465043i
$111$		0			0
$112$	−6.83224	−	9.17729i	−0.645586	−	0.867173i
$113$	5.97717	+	1.41662i	0.562285	+	0.133264i	0.501923	−	0.864913i	$-0.332626\pi$
$113$	5.97717	+	1.41662i	0.562285	+	0.133264i	0.0603623	+	0.998177i	$0.480774\pi$
$114$		0			0
$115$	−4.08619	+	5.48871i	−0.381039	+	0.511825i
$116$	9.07847	−	7.61774i	0.842915	−	0.707289i
$117$		0			0
$118$	3.48172	+	2.92151i	0.320518	+	0.268946i
$119$	13.5611	−	3.21403i	1.24314	−	0.294629i
$120$		0			0
$121$	7.20044	+	4.73580i	0.654586	+	0.430528i
$122$	−23.2017	−	15.2600i	−2.10058	−	1.38157i
$123$		0			0
$124$	−1.83451	+	0.434786i	−0.164744	+	0.0390450i
$125$	6.06083	+	5.08564i	0.542097	+	0.454873i
$126$		0			0
$127$	−0.493451	+	0.414054i	−0.0437867	+	0.0367414i	−0.664418	−	0.747361i	$-0.731321\pi$
$127$	−0.493451	+	0.414054i	−0.0437867	+	0.0367414i	0.620632	+	0.784102i	$0.286876\pi$
$128$	0.430598	−	0.578393i	0.0380598	−	0.0511232i
$129$		0			0
$130$	−14.5738	−	3.45405i	−1.27820	−	0.302940i
$131$	−0.462286	−	0.620957i	−0.0403901	−	0.0542533i	0.781469	−	0.623944i	$-0.214471\pi$
$131$	−0.462286	−	0.620957i	−0.0403901	−	0.0542533i	−0.821859	+	0.569690i	$0.807063\pi$
$132$		0			0
$133$	16.1265	+	8.09902i	1.39834	+	0.702274i
$134$	2.02921	−	3.51470i	0.175297	−	0.303624i
$135$		0			0
$136$	0.214610	+	0.371715i	0.0184026	+	0.0318743i
$137$	0.185518	+	3.18522i	0.0158499	+	0.272132i	0.996917	+	0.0784636i	$0.0250014\pi$
$137$	0.185518	+	3.18522i	0.0158499	+	0.272132i	−0.981067	+	0.193668i	$0.937962\pi$
$138$		0			0
$139$	−21.3695	+	2.49773i	−1.81253	+	0.211855i	−0.953774	−	0.300524i	$-0.902838\pi$
$139$	−21.3695	+	2.49773i	−1.81253	+	0.211855i	−0.858759	+	0.512379i	$0.828764\pi$
$140$	−6.01121	−	20.0788i	−0.508040	−	1.69697i
$141$		0			0
$142$	−0.193670	−	0.448979i	−0.0162525	−	0.0376775i
$143$	−3.08450	−	1.12267i	−0.257939	−	0.0938820i
$144$		0			0
$145$	−19.0689	+	6.94053i	−1.58359	+	0.576379i
$146$	−6.40710	−	6.79113i	−0.530255	−	0.562038i
$147$		0			0
$148$	6.23038	−	3.12901i	0.512134	−	0.257203i
$149$	−0.689615	+	11.8402i	−0.0564955	+	0.969990i	0.844334	+	0.535817i	$0.179996\pi$
$149$	−0.689615	+	11.8402i	−0.0564955	+	0.969990i	−0.900830	+	0.434173i	$0.857041\pi$
$150$		0			0
$151$	4.70339	−	15.7104i	0.382757	−	1.27850i	−0.522138	−	0.852861i	$-0.674865\pi$
$151$	4.70339	−	15.7104i	0.382757	−	1.27850i	0.904895	−	0.425635i	$-0.139949\pi$
$152$	−0.0965094	+	0.547332i	−0.00782795	+	0.0443945i
$153$		0			0
$154$	−1.57779	−	8.94812i	−0.127142	−	0.721060i
$155$	3.20643	+	0.374778i	0.257547	+	0.0301029i
$156$		0			0
$157$	−3.87444	+	4.10667i	−0.309214	+	0.327748i	−0.863280	−	0.504725i	$-0.831594\pi$
$157$	−3.87444	+	4.10667i	−0.309214	+	0.327748i	0.554066	+	0.832473i	$0.313075\pi$
$158$	2.53264	−	5.87133i	0.201486	−	0.467098i
$159$		0			0
$160$	−23.5218	+	15.4705i	−1.85956	+	1.22305i
$161$	−5.72100			−0.450878
$162$		0			0
$163$	−3.70178			−0.289946			−0.144973	−	0.989436i	$-0.546310\pi$
$163$	−3.70178			−0.289946			−0.144973	+	0.989436i	$0.546310\pi$
$164$	15.1338	−	9.95365i	1.18175	−	0.777249i
$165$		0			0
$166$	−11.7374	+	27.2103i	−0.910996	+	2.11193i
$167$	−0.200037	+	0.212027i	−0.0154793	+	0.0164071i	−0.735067	−	0.677994i	$-0.762849\pi$
$167$	−0.200037	+	0.212027i	−0.0154793	+	0.0164071i	0.719588	+	0.694402i	$0.244331\pi$
$168$		0			0
$169$	8.41891	+	0.984030i	0.647609	+	0.0756946i
$170$	−5.82154	−	33.0156i	−0.446492	−	2.53218i
$171$		0			0
$172$	−1.56811	+	8.89318i	−0.119567	+	0.678099i
$173$	1.58382	−	5.29033i	0.120416	−	0.402216i	−0.876435	−	0.481520i	$-0.840085\pi$
$173$	1.58382	−	5.29033i	0.120416	−	0.402216i	0.996850	+	0.0793044i	$0.0252699\pi$
$174$		0			0
$175$	−1.23569	+	21.2159i	−0.0934091	+	1.60377i
$176$	−5.39013	+	2.70702i	−0.406296	+	0.204050i
$177$		0			0
$178$	14.3063	+	15.1638i	1.07231	+	1.13658i
$179$	12.6675	−	4.61058i	0.946811	−	0.344611i	0.177959	−	0.984038i	$-0.443051\pi$
$179$	12.6675	−	4.61058i	0.946811	−	0.344611i	0.768852	+	0.639427i	$0.220828\pi$
$180$		0			0
$181$	23.6304	+	8.60076i	1.75643	+	0.639289i	0.999893	−	0.0146584i	$-0.00466609\pi$
$181$	23.6304	+	8.60076i	1.75643	+	0.639289i	0.756540	+	0.653948i	$0.226888\pi$
$182$	−4.95981	−	11.4981i	−0.367645	−	0.852298i
$183$		0			0
$184$	−0.0505330	−	0.168792i	−0.00372534	−	0.0124435i
$185$	−11.8574	+	1.38594i	−0.871776	+	0.101896i
$186$		0			0
$187$	−0.427207	−	7.33485i	−0.0312404	−	0.536378i
$188$	−6.44319	−	11.1599i	−0.469918	−	0.813922i
$189$		0			0
$190$	21.7049	−	37.5939i	1.57464	−	2.72735i
$191$	12.7490	+	6.40276i	0.922482	+	0.463288i	0.845639	−	0.533755i	$-0.179220\pi$
$191$	12.7490	+	6.40276i	0.922482	+	0.463288i	0.0768429	+	0.997043i	$0.475516\pi$
$192$		0			0
$193$	1.71320	+	2.30123i	0.123319	+	0.165646i	0.859495	−	0.511144i	$-0.170778\pi$
$193$	1.71320	+	2.30123i	0.123319	+	0.165646i	−0.736176	+	0.676790i	$0.763371\pi$
$194$	25.9138	+	6.14168i	1.86050	+	0.440947i
$195$		0			0
$196$	1.91670	−	2.57457i	0.136907	−	0.183898i
$197$	−1.66429	+	1.39651i	−0.118576	+	0.0994971i	−0.700148	−	0.713998i	$-0.746882\pi$
$197$	−1.66429	+	1.39651i	−0.118576	+	0.0994971i	0.581572	+	0.813495i	$0.302438\pi$
$198$		0			0
$199$	−11.4628	−	9.61839i	−0.812573	−	0.681830i	0.138647	−	0.990342i	$-0.455725\pi$
$199$	−11.4628	−	9.61839i	−0.812573	−	0.681830i	−0.951220	+	0.308512i	$0.900169\pi$
$200$	−0.636867	+	0.150940i	−0.0450333	+	0.0106731i
$201$		0			0
$202$	−7.10021	−	4.66988i	−0.499569	−	0.328572i
$203$	−14.1750	−	9.32306i	−0.994892	−	0.654351i
$204$		0			0
$205$	−30.1802	+	7.15284i	−2.10788	+	0.499576i
$206$	9.12159	+	7.65393i	0.635532	+	0.533274i
$207$		0			0
$208$	−6.36790	+	5.34330i	−0.441534	+	0.370491i
$209$	5.68115	−	7.63111i	0.392973	−	0.527855i
$210$		0			0
$211$	11.6750	+	2.76702i	0.803739	+	0.190490i	0.611898	−	0.790936i	$-0.290406\pi$
$211$	11.6750	+	2.76702i	0.803739	+	0.190490i	0.191841	+	0.981426i	$0.438554\pi$
$212$	10.2557	+	13.7758i	0.704367	+	0.946129i
$213$		0			0
$214$	−1.48566	−	0.746129i	−0.101558	−	0.0510043i
$215$	7.73139	−	13.3912i	0.527277	−	0.913270i
$216$		0			0
$217$	1.34953	+	2.33745i	0.0916119	+	0.158676i
$218$	1.17726	+	20.2128i	0.0797343	+	1.36899i
$219$		0			0
$220$	−10.9748	+	1.28277i	−0.739922	+	0.0864845i
$221$	−2.90411	−	9.70040i	−0.195352	−	0.652520i
$222$		0			0
$223$	3.50410	+	8.12343i	0.234652	+	0.543985i	0.994333	−	0.106311i	$-0.0339040\pi$
$223$	3.50410	+	8.12343i	0.234652	+	0.543985i	−0.759681	+	0.650296i	$0.774645\pi$
$224$	−22.1187	−	8.05055i	−1.47787	−	0.537900i
$225$		0			0
$226$	11.6091	−	4.22537i	0.772226	−	0.281067i
$227$	12.3070	+	13.0446i	0.816841	+	0.865801i	0.992946	−	0.118570i	$-0.0378311\pi$
$227$	12.3070	+	13.0446i	0.816841	+	0.865801i	−0.176104	+	0.984372i	$0.556350\pi$
$228$		0			0
$229$	−5.60209	+	2.81348i	−0.370197	+	0.185920i	−0.624165	−	0.781293i	$-0.714561\pi$
$229$	−5.60209	+	2.81348i	−0.370197	+	0.185920i	0.253968	+	0.967213i	$0.418264\pi$
$230$	−0.800185	+	13.7386i	−0.0527626	+	0.905899i
$231$		0			0
$232$	0.149860	−	0.500569i	0.00983882	−	0.0328639i
$233$	−0.389839	+	2.21089i	−0.0255392	+	0.144840i	−0.994911	−	0.100758i	$-0.967873\pi$
$233$	−0.389839	+	2.21089i	−0.0255392	+	0.144840i	0.969372	+	0.245598i	$0.0789843\pi$
$234$		0			0
$235$	3.83163	+	21.7302i	0.249948	+	1.41753i
$236$	4.58986	+	0.536478i	0.298775	+	0.0349217i
$237$		0			0
$238$	19.2348	−	20.3877i	1.24681	−	1.32154i
$239$	−7.55947	+	17.5248i	−0.488981	+	1.13359i	0.477912	+	0.878407i	$0.341394\pi$
$239$	−7.55947	+	17.5248i	−0.488981	+	1.13359i	−0.966894	+	0.255179i	$0.917866\pi$
$240$		0			0
$241$	15.5225	−	10.2093i	0.999892	−	0.657639i	0.0596757	−	0.998218i	$-0.480993\pi$
$241$	15.5225	−	10.2093i	0.999892	−	0.657639i	0.940216	+	0.340579i	$0.110623\pi$
$242$	17.3328			1.11420
$243$		0			0
$244$	−28.2349			−1.80755
$245$	−4.59183	+	3.02009i	−0.293361	+	0.192947i
$246$		0			0
$247$	5.19316	−	12.0391i	0.330433	−	0.766029i
$248$	−0.0570438	+	0.0604628i	−0.00362228	+	0.00383939i
$249$		0			0
$250$	15.8045	+	1.84728i	0.999566	+	0.116833i
$251$	1.93377	+	10.9669i	0.122058	+	0.692227i	0.983012	+	0.183543i	$0.0587568\pi$
$251$	1.93377	+	10.9669i	0.122058	+	0.692227i	−0.860953	+	0.508684i	$0.830132\pi$
$252$		0			0
$253$	−0.523732	+	2.97023i	−0.0329267	+	0.186737i
$254$	−0.371556	+	1.24108i	−0.0233135	+	0.0778724i
$255$		0			0
$256$	−0.887221	+	15.2330i	−0.0554513	+	0.952063i
$257$	−16.8394	+	8.45708i	−1.05041	+	0.527538i	−0.888314	−	0.459236i	$-0.848123\pi$
$257$	−16.8394	+	8.45708i	−1.05041	+	0.527538i	−0.162100	+	0.986774i	$0.551827\pi$
$258$		0			0
$259$	−6.84948	−	7.26002i	−0.425606	−	0.451116i
$260$	−14.3097	+	5.20832i	−0.887453	+	0.323006i
$261$		0			0
$262$	−1.46304	−	0.532503i	−0.0903870	−	0.0328982i
$263$	−5.71184	−	13.2415i	−0.352207	−	0.816508i	−0.998569	−	0.0534771i	$-0.982970\pi$
$263$	−5.71184	−	13.2415i	−0.352207	−	0.816508i	0.646362	−	0.763031i	$-0.276290\pi$
$264$		0			0
$265$	−8.43419	−	28.1721i	−0.518108	−	1.73060i
$266$	36.0482	−	4.21343i	2.21026	−	0.258342i
$267$		0			0
$268$	−0.239925	−	4.11935i	−0.0146558	−	0.251630i
$269$	−10.2460	−	17.7466i	−0.624712	−	1.08203i	−0.988597	−	0.150588i	$-0.951883\pi$
$269$	−10.2460	−	17.7466i	−0.624712	−	1.08203i	0.363885	−	0.931444i	$-0.381450\pi$
$270$		0			0
$271$	7.82529	−	13.5538i	0.475353	−	0.823335i	−0.524249	−	0.851565i	$-0.675654\pi$
$271$	7.82529	−	13.5538i	0.475353	−	0.823335i	0.999601	+	0.0282303i	$0.00898716\pi$
$272$	−16.6276	−	8.35069i	−1.00820	−	0.506335i
$273$		0			0
$274$	3.83190	+	5.14714i	0.231494	+	0.310950i
$275$	10.9017	+	2.58376i	0.657400	+	0.155807i
$276$		0			0
$277$	−12.0941	+	16.2451i	−0.726661	+	0.976076i	0.273239	+	0.961946i	$0.411905\pi$
$277$	−12.0941	+	16.2451i	−0.726661	+	0.976076i	−0.999900	+	0.0141295i	$0.995502\pi$
$278$	−33.1470	+	27.8136i	−1.98802	+	1.66815i
$279$		0			0
$280$	−0.707906	−	0.594004i	−0.0423055	−	0.0354985i
$281$	−12.9680	+	3.07347i	−0.773605	+	0.183348i	−0.598415	−	0.801187i	$-0.704202\pi$
$281$	−12.9680	+	3.07347i	−0.773605	+	0.183348i	−0.175191	+	0.984534i	$0.556054\pi$
$282$		0			0
$283$	25.5751	+	16.8210i	1.52028	+	0.999904i	0.988193	+	0.153214i	$0.0489622\pi$
$283$	25.5751	+	16.8210i	1.52028	+	0.999904i	0.532086	+	0.846690i	$0.321408\pi$
$284$	−0.415363	−	0.273188i	−0.0246473	−	0.0162108i
$285$		0			0
$286$	−6.42365	+	1.52243i	−0.379838	+	0.0900233i
$287$	−19.8649	−	16.6686i	−1.17259	−	0.983918i
$288$		0			0
$289$	4.33970	−	3.64144i	0.255276	−	0.214202i
$290$	−24.3714	+	32.7365i	−1.43114	+	1.92235i
$291$		0			0
$292$	−9.23685	−	2.18917i	−0.540546	−	0.128112i
$293$	−10.2547	−	13.7744i	−0.599085	−	0.804711i	0.394368	−	0.918953i	$-0.370964\pi$
$293$	−10.2547	−	13.7744i	−0.599085	−	0.804711i	−0.993453	+	0.114242i	$0.963556\pi$
$294$		0			0
$295$	−7.07110	−	3.55124i	−0.411696	−	0.206761i
$296$	0.153698	−	0.266213i	0.00893354	−	0.0154733i
$297$		0			0
$298$	11.9266	+	20.6574i	0.690888	+	1.19665i
$299$	0.241686	+	4.14959i	0.0139771	+	0.239977i
$300$		0			0
$301$	12.8406	−	1.50085i	0.740118	−	0.0865074i
$302$	−9.45935	−	31.5964i	−0.544324	−	1.81817i
$303$		0			0
$304$	−9.54273	−	22.1225i	−0.547313	−	1.26881i
$305$	45.4312	+	16.5356i	2.60138	+	0.946825i
$306$		0			0
$307$	−29.3001	+	10.6644i	−1.67225	+	0.608648i	−0.992215	−	0.124536i	$-0.960256\pi$
$307$	−29.3001	+	10.6644i	−1.67225	+	0.608648i	−0.680031	+	0.733184i	$0.738034\pi$
$308$	−6.33963	−	6.71962i	−0.361234	−	0.382886i
$309$		0			0
$310$	5.80200	−	2.91387i	0.329532	−	0.165497i
$311$	1.41160	−	24.2362i	0.0800444	−	1.37431i	−0.684159	−	0.729333i	$-0.739831\pi$
$311$	1.41160	−	24.2362i	0.0800444	−	1.37431i	0.764203	−	0.644975i	$-0.223132\pi$
$312$		0			0
$313$	0.792609	−	2.64750i	0.0448009	−	0.149646i	−0.932663	−	0.360750i	$-0.882521\pi$
$313$	0.792609	−	2.64750i	0.0448009	−	0.149646i	0.977464	+	0.211104i	$0.0677060\pi$
$314$	−1.97175	+	11.1824i	−0.111272	+	0.631058i
$315$		0			0
$316$	−1.12893	−	6.40250i	−0.0635075	−	0.360169i
$317$	−14.5673	−	1.70267i	−0.818182	−	0.0956317i	−0.303302	−	0.952894i	$-0.598089\pi$
$317$	−14.5673	−	1.70267i	−0.818182	−	0.0956317i	−0.514879	+	0.857263i	$0.672163\pi$
$318$		0			0
$319$	−6.13800	+	6.50590i	−0.343662	+	0.364261i
$320$	−11.5862	+	26.8599i	−0.647691	+	1.50152i
$321$		0			0
$322$	−9.61307	+	6.32262i	−0.535716	+	0.352346i
$323$	29.3479			1.63296
$324$		0			0
$325$	15.4406			0.856493
$326$	−6.22016	+	4.09106i	−0.344503	+	0.226583i
$327$		0			0
$328$	0.316326	−	0.733325i	0.0174662	−	0.0404911i
$329$	−12.6600	+	13.4188i	−0.697968	+	0.739803i
$330$		0			0
$331$	8.79405	+	1.02788i	0.483365	+	0.0564972i	0.354286	−	0.935137i	$-0.384724\pi$
$331$	8.79405	+	1.02788i	0.483365	+	0.0564972i	0.129079	+	0.991634i	$0.458798\pi$
$332$	5.23197	+	29.6720i	0.287142	+	1.62846i
$333$		0			0
$334$	−0.101801	+	0.577344i	−0.00557032	+	0.0315909i
$335$	−2.02643	+	6.76873i	−0.110715	+	0.369815i
$336$		0			0
$337$	1.54771	−	26.5732i	0.0843091	−	1.44753i	−0.645437	−	0.763814i	$-0.723325\pi$
$337$	1.54771	−	26.5732i	0.0843091	−	1.44753i	0.729746	−	0.683718i	$-0.239638\pi$
$338$	15.2339	−	7.65076i	0.828616	−	0.416147i
$339$		0			0
$340$	−23.3911	−	24.7932i	−1.26856	−	1.34460i
$341$	1.33710	−	0.486665i	0.0724081	−	0.0263544i
$342$		0			0
$343$	14.9381	+	5.43701i	0.806580	+	0.293571i
$344$	0.157700	+	0.365591i	0.00850263	+	0.0197113i
$345$		0			0
$346$	−3.18534	−	10.6398i	−0.171245	−	0.571998i
$347$	13.0631	−	1.52686i	0.701263	−	0.0819659i	0.242013	−	0.970273i	$-0.422192\pi$
$347$	13.0631	−	1.52686i	0.701263	−	0.0819659i	0.459250	+	0.888307i	$0.348118\pi$
$348$		0			0
$349$	−0.0382600	−	0.656898i	−0.00204801	−	0.0351630i	0.997129	−	0.0757173i	$-0.0241247\pi$
$349$	−0.0382600	−	0.656898i	−0.00204801	−	0.0351630i	−0.999177	+	0.0405543i	$0.987088\pi$
$350$	21.3706	+	37.0150i	1.14231	+	1.97853i
$351$		0			0
$352$	−6.20455	+	10.7466i	−0.330703	+	0.572795i
$353$	11.1809	+	5.61525i	0.595098	+	0.298869i	0.720739	−	0.693206i	$-0.243803\pi$
$353$	11.1809	+	5.61525i	0.595098	+	0.298869i	−0.125641	+	0.992076i	$0.540099\pi$
$354$		0			0
$355$	0.508346	+	0.682827i	0.0269802	+	0.0362407i
$356$	20.6249	+	4.88818i	1.09312	+	0.259073i
$357$		0			0
$358$	16.1899	−	21.7468i	0.855662	−	1.14935i
$359$	−13.4556	+	11.2906i	−0.710157	+	0.595893i	−0.924643	−	0.380834i	$-0.875637\pi$
$359$	−13.4556	+	11.2906i	−0.710157	+	0.595893i	0.214486	+	0.976727i	$0.431192\pi$
$360$		0			0
$361$	14.5557	+	12.2137i	0.766091	+	0.642827i
$362$	49.2116	−	11.6634i	2.58651	−	0.613013i
$363$		0			0
$364$	−10.6372	−	6.99623i	−0.557543	−	0.366702i
$365$	13.5804	+	8.93198i	0.710832	+	0.467521i
$366$		0			0
$367$	31.7494	−	7.52475i	1.65731	−	0.392789i	0.707768	−	0.706445i	$-0.249702\pi$
$367$	31.7494	−	7.52475i	1.65731	−	0.392789i	0.949537	+	0.313656i	$0.101554\pi$
$368$	5.85108	+	4.90964i	0.305009	+	0.255933i
$369$		0			0
$370$	−18.3925	+	15.4332i	−0.956182	+	0.802332i
$371$	14.6822	−	19.7216i	0.762263	−	1.02390i
$372$		0			0
$373$	1.97125	+	0.467194i	0.102067	+	0.0241904i	0.281332	−	0.959610i	$-0.409224\pi$
$373$	1.97125	+	0.467194i	0.102067	+	0.0241904i	−0.179265	+	0.983801i	$0.557372\pi$
$374$	−8.82402	−	11.8527i	−0.456279	−	0.612889i
$375$		0			0
$376$	−0.507732	−	0.254993i	−0.0261843	−	0.0131502i
$377$	−6.16343	+	10.6754i	−0.317433	+	0.549809i
$378$		0			0
$379$	−3.41848	−	5.92098i	−0.175596	−	0.304140i	0.764772	−	0.644301i	$-0.222852\pi$
$379$	−3.41848	−	5.92098i	−0.175596	−	0.304140i	−0.940367	+	0.340161i	$0.889518\pi$
$380$	−2.56629	−	44.0614i	−0.131648	−	2.26030i
$381$		0			0
$382$	28.4983	−	3.33097i	1.45810	−	0.170427i
$383$	−1.23865	−	4.13738i	−0.0632921	−	0.211410i	0.920494	−	0.390757i	$-0.127787\pi$
$383$	−1.23865	−	4.13738i	−0.0632921	−	0.211410i	−0.983786	+	0.179347i	$0.942602\pi$
$384$		0			0
$385$	6.26544	+	14.5249i	0.319316	+	0.740259i
$386$	5.42195	+	1.97343i	0.275970	+	0.100445i
$387$		0			0
$388$	25.4443	−	9.26097i	1.29174	−	0.470154i
$389$	10.8413	+	11.4911i	0.549677	+	0.582623i	0.941329	−	0.337490i	$-0.109578\pi$
$389$	10.8413	+	11.4911i	0.549677	+	0.582623i	−0.391652	+	0.920113i	$0.628096\pi$
$390$		0			0
$391$	−8.31434	+	4.17562i	−0.420474	+	0.211170i
$392$	0.00822846	−	0.141277i	0.000415600	−	0.00713558i
$393$		0			0
$394$	−1.25317	+	4.18588i	−0.0631338	+	0.210882i
$395$	−1.93308	+	10.9631i	−0.0972639	+	0.551611i
$396$		0			0
$397$	−3.34977	−	18.9975i	−0.168120	−	0.953458i	−0.945789	−	0.324783i	$-0.894709\pi$
$397$	−3.34977	−	18.9975i	−0.168120	−	0.953458i	0.777668	−	0.628675i	$-0.216402\pi$
$398$	−29.8909	−	3.49374i	−1.49829	−	0.175125i
$399$		0			0
$400$	19.4708	−	20.6378i	0.973540	−	1.03189i
$401$	−8.42863	+	19.5398i	−0.420906	+	0.975769i	0.567422	+	0.823427i	$0.307941\pi$
$401$	−8.42863	+	19.5398i	−0.420906	+	0.975769i	−0.988328	+	0.152342i	$0.951318\pi$
$402$		0			0
$403$	1.63840	−	1.07759i	0.0816146	−	0.0536788i
$404$	−8.64048			−0.429880
$405$		0			0
$406$	−34.1219			−1.69344
$407$	−4.39629	+	2.89149i	−0.217916	+	0.143326i
$408$		0			0
$409$	−5.55599	+	12.8802i	−0.274726	+	0.636886i	−0.998592	−	0.0530546i	$-0.983104\pi$
$409$	−5.55599	+	12.8802i	−0.274726	+	0.636886i	0.723866	+	0.689941i	$0.242364\pi$
$410$	−42.8072	+	45.3729i	−2.11410	+	2.24081i
$411$		0			0
$412$	12.0248	+	1.40549i	0.592418	+	0.0692438i
$413$	−1.14879	−	6.51512i	−0.0565284	−	0.320588i
$414$		0			0
$415$	8.95874	−	50.8076i	0.439767	−	2.49405i
$416$	−4.90486	+	16.3834i	−0.240480	+	0.803260i
$417$		0			0
$418$	1.11252	−	19.1012i	0.0544151	−	0.934272i
$419$	20.4759	−	10.2834i	1.00031	−	0.502377i	0.128237	−	0.991744i	$-0.459068\pi$
$419$	20.4759	−	10.2834i	1.00031	−	0.502377i	0.872078	+	0.489367i	$0.162772\pi$
$420$		0			0
$421$	5.45757	+	5.78468i	0.265986	+	0.281928i	0.846576	−	0.532267i	$-0.178660\pi$
$421$	5.45757	+	5.78468i	0.265986	+	0.281928i	−0.580591	+	0.814196i	$0.697178\pi$
$422$	22.6756	−	8.25325i	1.10383	−	0.401762i
$423$		0			0
$424$	0.711553	+	0.258984i	0.0345561	+	0.0125774i
$425$	13.6891	+	31.7350i	0.664021	+	1.53937i
$426$		0			0
$427$	11.5930	+	38.7233i	0.561024	+	1.87395i
$428$	−1.67889	+	0.196234i	−0.0811521	+	0.00948532i
$429$		0			0
$430$	−1.80821	−	31.0458i	−0.0871997	−	1.49716i
$431$	−13.6391	−	23.6236i	−0.656971	−	1.13791i	−0.981396	−	0.191995i	$-0.938504\pi$
$431$	−13.6391	−	23.6236i	−0.656971	−	1.13791i	0.324425	−	0.945911i	$-0.394829\pi$
$432$		0			0
$433$	−12.6314	+	21.8783i	−0.607028	+	1.05140i	0.384699	+	0.923042i	$0.374305\pi$
$433$	−12.6314	+	21.8783i	−0.607028	+	1.05140i	−0.991727	+	0.128362i	$0.959028\pi$
$434$	4.85088	+	2.43621i	0.232850	+	0.116942i
$435$		0			0
$436$	12.2930	+	16.5124i	0.588729	+	0.790801i
$437$	−11.7225	−	2.77829i	−0.560765	−	0.132904i
$438$		0			0
$439$	21.1198	−	28.3689i	1.00799	−	1.35397i	0.0737750	−	0.997275i	$-0.476495\pi$
$439$	21.1198	−	28.3689i	1.00799	−	1.35397i	0.934220	−	0.356697i	$-0.116097\pi$
$440$	−0.373200	+	0.313152i	−0.0177916	+	0.0149290i
$441$		0			0
$442$	−15.6003	−	13.0902i	−0.742031	−	0.622638i
$443$	−30.2688	+	7.17384i	−1.43811	+	0.340839i	−0.874430	−	0.485151i	$-0.838765\pi$
$443$	−30.2688	+	7.17384i	−1.43811	+	0.340839i	−0.563684	+	0.825991i	$0.690616\pi$
$444$		0			0
$445$	−30.3236	−	19.9441i	−1.43748	−	0.945443i
$446$	14.8657	+	9.77731i	0.703910	+	0.462969i
$447$		0			0
$448$	−23.7978	+	5.64017i	−1.12434	+	0.266473i
$449$	−4.29232	−	3.60169i	−0.202567	−	0.169974i	0.535861	−	0.844306i	$-0.319987\pi$
$449$	−4.29232	−	3.60169i	−0.202567	−	0.169974i	−0.738428	+	0.674332i	$0.764432\pi$
$450$		0			0
$451$	−10.4726	+	8.78752i	−0.493134	+	0.413788i
$452$	7.50083	−	10.0754i	0.352809	−	0.473905i
$453$		0			0
$454$	35.0959	+	8.31788i	1.64713	+	0.390378i
$455$	13.0185	+	17.4869i	0.610316	+	0.819797i
$456$		0			0
$457$	−16.7344	−	8.40435i	−0.782804	−	0.393139i	0.0120593	−	0.999927i	$-0.496161\pi$
$457$	−16.7344	−	8.40435i	−0.782804	−	0.393139i	−0.794864	+	0.606788i	$0.792458\pi$
$458$	−6.30393	+	10.9187i	−0.294563	+	0.510199i
$459$		0			0
$460$	6.99610	+	12.1176i	0.326195	+	0.564986i
$461$	0.911793	+	15.6549i	0.0424664	+	0.729120i	0.950596	+	0.310431i	$0.100473\pi$
$461$	0.911793	+	15.6549i	0.0424664	+	0.729120i	−0.908130	+	0.418689i	$0.862490\pi$
$462$		0			0
$463$	2.95247	−	0.345094i	0.137213	−	0.0160379i	−0.0472091	−	0.998885i	$-0.515033\pi$
$463$	2.95247	−	0.345094i	0.137213	−	0.0160379i	0.184422	+	0.982847i	$0.440959\pi$
$464$	6.49647	+	21.6997i	0.301591	+	1.00738i
$465$		0			0
$466$	1.78833	+	4.14581i	0.0828427	+	0.192051i
$467$	−7.67714	−	2.79425i	−0.355256	−	0.129302i	0.158226	−	0.987403i	$-0.449422\pi$
$467$	−7.67714	−	2.79425i	−0.355256	−	0.129302i	−0.513482	+	0.858100i	$0.671645\pi$
$468$		0			0
$469$	−5.55105	+	2.02042i	−0.256324	+	0.0932943i
$470$	30.4537	+	32.2791i	1.40473	+	1.48892i
$471$		0			0
$472$	0.182075	−	0.0914413i	0.00838066	−	0.00420893i
$473$	0.396286	−	6.80396i	0.0182212	−	0.312847i
$474$		0			0
$475$	−12.8350	+	42.8720i	−0.588912	+	1.96710i
$476$	4.94866	−	28.0652i	0.226821	−	1.28637i
$477$		0			0
$478$	6.66544	+	37.8016i	0.304870	+	1.72900i
$479$	0.787677	+	0.0920663i	0.0359899	+	0.00420662i	0.134069	−	0.990972i	$-0.457196\pi$
$479$	0.787677	+	0.0920663i	0.0359899	+	0.00420662i	−0.0980789	+	0.995179i	$0.531270\pi$
$480$		0			0
$481$	−4.97652	+	5.27480i	−0.226910	+	0.240510i
$482$	14.7997	−	34.3097i	0.674110	−	1.56276i
$483$		0			0
$484$	14.7237	−	9.68391i	0.669257	−	0.440178i
$485$	−46.3646			−2.10531
$486$		0			0
$487$	2.96218			0.134229			0.0671145	−	0.997745i	$-0.478621\pi$
$487$	2.96218			0.134229			0.0671145	+	0.997745i	$0.478621\pi$
$488$	−1.04009	+	0.684077i	−0.0470826	+	0.0309667i
$489$		0			0
$490$	−4.37802	+	10.1494i	−0.197779	+	0.458503i
$491$	2.29668	−	2.43433i	0.103647	−	0.109860i	−0.673473	−	0.739212i	$-0.735198\pi$
$491$	2.29668	−	2.43433i	0.103647	−	0.109860i	0.777120	+	0.629352i	$0.216680\pi$
$492$		0			0
$493$	−27.4053	−	3.20322i	−1.23427	−	0.144266i
$494$	−4.57898	−	25.9687i	−0.206018	−	1.16839i
$495$		0			0
$496$	0.625737	−	3.54873i	0.0280964	−	0.159343i
$497$	−0.204125	+	0.681826i	−0.00915627	+	0.0305841i
$498$		0			0
$499$	1.11187	−	19.0902i	0.0497744	−	0.854593i	−0.877353	−	0.479846i	$-0.840693\pi$
$499$	1.11187	−	19.0902i	0.0497744	−	0.854593i	0.927127	−	0.374747i	$-0.122270\pi$
$500$	14.4575	−	7.26084i	0.646560	−	0.324715i
$501$		0			0
$502$	15.3696	+	16.2908i	0.685977	+	0.727093i
$503$	−4.78792	+	1.74266i	−0.213483	+	0.0777013i	−0.446548	−	0.894760i	$-0.647347\pi$
$503$	−4.78792	+	1.74266i	−0.213483	+	0.0777013i	0.233065	+	0.972461i	$0.425124\pi$
$504$		0			0
$505$	13.9029	+	5.06024i	0.618671	+	0.225178i
$506$	2.40254	+	5.56972i	0.106806	+	0.247604i
$507$		0			0
$508$	0.377773	+	1.26185i	0.0167610	+	0.0559855i
$509$	−28.8924	+	3.37704i	−1.28064	+	0.149685i	−0.729065	−	0.684444i	$-0.760045\pi$
$509$	−28.8924	+	3.37704i	−1.28064	+	0.149685i	−0.551570	+	0.834129i	$0.685971\pi$
$510$		0			0
$511$	0.790182	+	13.5669i	0.0349556	+	0.600165i
$512$	16.0652	+	27.8257i	0.709987	+	1.22973i
$513$		0			0
$514$	−18.9491	+	32.8208i	−0.835809	+	1.44766i
$515$	−18.5253	−	9.30374i	−0.816321	−	0.409972i
$516$		0			0
$517$	5.80781	+	7.80124i	0.255427	+	0.343098i
$518$	−19.5327	−	4.62934i	−0.858219	−	0.203402i
$519$		0			0
$520$	−0.400941	+	0.538557i	−0.0175824	+	0.0236173i
$521$	11.5729	−	9.71080i	0.507017	−	0.425438i	−0.353061	−	0.935600i	$-0.614859\pi$
$521$	11.5729	−	9.71080i	0.507017	−	0.425438i	0.860078	+	0.510162i	$0.170415\pi$
$522$		0			0
$523$	27.5658	+	23.1305i	1.20537	+	1.01142i	0.999460	+	0.0328530i	$0.0104593\pi$
$523$	27.5658	+	23.1305i	1.20537	+	1.01142i	0.205908	+	0.978571i	$0.433985\pi$
$524$	−1.54032	+	0.365062i	−0.0672891	+	0.0159478i
$525$		0			0
$526$	−24.2317	−	15.9374i	−1.05655	−	0.694905i
$527$	3.66732	+	2.41203i	0.159751	+	0.105070i
$528$		0			0
$529$	−18.6637	+	4.42338i	−0.811466	+	0.192321i
$530$	−45.3068	−	38.0169i	−1.96800	−	1.65135i
$531$		0			0
$532$	28.2677	−	23.7194i	1.22556	−	1.02837i
$533$	−11.2510	+	15.1127i	−0.487334	+	0.654604i
$534$		0			0
$535$	2.81633	+	0.667482i	0.121760	+	0.0288578i
$536$	−0.108642	−	0.145932i	−0.00469263	−	0.00630329i
$537$		0			0
$538$	−36.8294	−	18.4964i	−1.58783	−	0.797437i
$539$	−1.21122	+	2.09790i	−0.0521711	+	0.0903631i
$540$		0			0
$541$	−4.71569	−	8.16782i	−0.202743	−	0.351162i	0.746668	−	0.665197i	$-0.231652\pi$
$541$	−4.71569	−	8.16782i	−0.202743	−	0.351162i	−0.949411	+	0.314035i	$0.898319\pi$
$542$	−1.83017	−	31.4228i	−0.0786126	−	1.34973i
$543$		0			0
$544$	−38.0210	+	4.44402i	−1.63014	+	0.190536i
$545$	−10.1096	−	33.7685i	−0.433049	−	1.44648i
$546$		0			0
$547$	10.4616	+	24.2528i	0.447307	+	1.03698i	0.981474	+	0.191596i	$0.0613663\pi$
$547$	10.4616	+	24.2528i	0.447307	+	1.03698i	−0.534166	+	0.845379i	$0.679374\pi$
$548$	6.13080	+	2.23143i	0.261895	+	0.0953220i
$549$		0			0
$550$	21.1738	−	7.70664i	0.902855	−	0.328612i
$551$	−24.5176	−	25.9871i	−1.04448	−	1.10709i
$552$		0			0
$553$	−8.31730	+	4.17710i	−0.353687	+	0.177629i
$554$	−2.36834	+	40.6628i	−0.100621	+	1.72760i
$555$		0			0
$556$	−12.6177	+	42.1461i	−0.535110	+	1.78739i
$557$	3.82840	−	21.7119i	0.162215	−	0.919964i	−0.789676	−	0.613525i	$-0.789751\pi$
$557$	3.82840	−	21.7119i	0.162215	−	0.919964i	0.951890	−	0.306440i	$-0.0991378\pi$
$558$		0			0
$559$	−1.63106	−	9.25019i	−0.0689864	−	0.391242i
$560$	39.7893	+	4.65070i	1.68140	+	0.196528i
$561$		0			0
$562$	−18.3936	+	19.4961i	−0.775887	+	0.822393i
$563$	−3.08543	+	7.15282i	−0.130035	+	0.301455i	−0.970778	−	0.239979i	$-0.922859\pi$
$563$	−3.08543	+	7.15282i	−0.130035	+	0.301455i	0.840743	+	0.541435i	$0.182119\pi$
$564$		0			0
$565$	−17.9697	+	11.8189i	−0.755992	+	0.497224i
$566$	61.5640			2.58773
$567$		0			0
$568$	−0.0219196			−0.000919724
$569$	24.2334	−	15.9386i	1.01592	−	0.668179i	0.0716740	−	0.997428i	$-0.477166\pi$
$569$	24.2334	−	15.9386i	1.01592	−	0.668179i	0.944243	+	0.329249i	$0.106796\pi$
$570$		0			0
$571$	5.97798	−	13.8585i	0.250171	−	0.579961i	−0.746139	−	0.665790i	$-0.768095\pi$
$571$	5.97798	−	13.8585i	0.250171	−	0.579961i	0.996310	+	0.0858293i	$0.0273540\pi$
$572$	−4.60609	+	4.88217i	−0.192590	+	0.204134i
$573$		0			0
$574$	−51.8007	−	6.05464i	−2.16212	−	0.252716i
$575$	−2.46363	−	13.9719i	−0.102740	−	0.582670i
$576$		0			0
$577$	−2.67015	+	15.1432i	−0.111160	+	0.630419i	0.877420	+	0.479723i	$0.159263\pi$
$577$	−2.67015	+	15.1432i	−0.111160	+	0.630419i	−0.988580	+	0.150696i	$0.951848\pi$
$578$	3.26768	−	10.9148i	0.135918	−	0.453997i
$579$		0			0
$580$	−2.41273	+	41.4250i	−0.100183	+	1.72008i
$581$	38.5460	−	19.3585i	1.59916	−	0.803126i
$582$		0			0
$583$	−8.89499	−	9.42814i	−0.368393	−	0.390474i
$584$	−0.393297	+	0.143149i	−0.0162748	+	0.00592353i
$585$		0			0
$586$	−32.4540	−	11.8123i	−1.34066	−	0.487962i
$587$	13.6772	+	31.7072i	0.564517	+	1.30870i	0.926423	+	0.376483i	$0.122867\pi$
$587$	13.6772	+	31.7072i	0.564517	+	1.30870i	−0.361906	+	0.932214i	$0.617874\pi$
$588$		0			0
$589$	1.63009	+	5.44489i	0.0671668	+	0.224353i
$590$	−15.8064	+	1.84750i	−0.650737	+	0.0760603i
$591$		0			0
$592$	0.774821	+	13.3032i	0.0318449	+	0.546756i
$593$	9.59352	+	16.6165i	0.393959	+	0.682357i	0.992968	−	0.118386i	$-0.0377719\pi$
$593$	9.59352	+	16.6165i	0.393959	+	0.682357i	−0.599009	+	0.800742i	$0.704439\pi$
$594$		0			0
$595$	−24.3988	+	42.2600i	−1.00026	+	1.73249i
$596$	21.6726	+	10.8844i	0.887745	+	0.445843i
$597$		0			0
$598$	4.99207	+	6.70551i	0.204141	+	0.274209i
$599$	−30.4840	−	7.22483i	−1.24554	−	0.295199i	−0.445575	−	0.895244i	$-0.647001\pi$
$599$	−30.4840	−	7.22483i	−1.24554	−	0.295199i	−0.799966	+	0.600046i	$0.795149\pi$
$600$		0			0
$601$	−22.6964	+	30.4866i	−0.925805	+	1.24357i	0.0438355	+	0.999039i	$0.486042\pi$
$601$	−22.6964	+	30.4866i	−0.925805	+	1.24357i	−0.969641	+	0.244534i	$0.921365\pi$
$602$	19.9175	−	16.7128i	0.811777	−	0.681162i
$603$		0			0
$604$	−25.6885	−	21.5552i	−1.04525	−	0.877068i
$605$	−29.3623	+	6.95900i	−1.19375	+	0.282924i
$606$		0			0
$607$	12.2471	+	8.05506i	0.497096	+	0.326945i	0.773178	−	0.634189i	$-0.218666\pi$
$607$	12.2471	+	8.05506i	0.497096	+	0.326945i	−0.276082	+	0.961134i	$0.589036\pi$
$608$	−41.4124	−	27.2374i	−1.67949	−	1.10462i
$609$		0			0
$610$	94.6130	−	22.4237i	3.83077	−	0.907909i
$611$	10.2678	+	8.61573i	0.415392	+	0.348555i
$612$		0			0
$613$	21.4111	−	17.9661i	0.864787	−	0.725642i	−0.0982069	−	0.995166i	$-0.531311\pi$
$613$	21.4111	−	17.9661i	0.864787	−	0.725642i	0.962994	+	0.269524i	$0.0868663\pi$
$614$	−37.4475	+	50.3008i	−1.51126	+	2.02997i
$615$		0			0
$616$	−0.396337	−	0.0939335i	−0.0159689	−	0.00378469i
$617$	15.9682	+	21.4491i	0.642857	+	0.863507i	0.997439	−	0.0715181i	$-0.0227844\pi$
$617$	15.9682	+	21.4491i	0.642857	+	0.863507i	−0.354582	+	0.935025i	$0.615377\pi$
$618$		0			0
$619$	−4.10387	−	2.06104i	−0.164948	−	0.0828402i	0.364410	−	0.931239i	$-0.381271\pi$
$619$	−4.10387	−	2.06104i	−0.164948	−	0.0828402i	−0.529358	+	0.848399i	$0.677567\pi$
$620$	3.30062	−	5.71684i	0.132556	−	0.229594i
$621$		0			0
$622$	−24.4129	−	42.2844i	−0.978869	−	1.69545i
$623$	−1.76439	−	30.2934i	−0.0706888	−	1.21368i
$624$		0			0
$625$	8.53771	−	0.997916i	0.341509	−	0.0399166i
$626$	−1.59408	−	5.32459i	−0.0637121	−	0.212813i
$627$		0			0
$628$	4.57269	+	10.6007i	0.182470	+	0.423013i
$629$	−15.2533	−	5.55173i	−0.608187	−	0.221362i
$630$		0			0
$631$	27.3628	−	9.95925i	1.08930	−	0.396471i	0.265936	−	0.963991i	$-0.414319\pi$
$631$	27.3628	−	9.95925i	1.08930	−	0.396471i	0.823360	+	0.567519i	$0.192097\pi$
$632$	−0.196707	−	0.208497i	−0.00782458	−	0.00829357i
$633$		0			0
$634$	−26.3594	+	13.2382i	−1.04686	+	0.525755i
$635$	0.131141	−	2.25161i	0.00520419	−	0.0893525i
$636$		0			0
$637$	−0.957505	+	3.19829i	−0.0379377	+	0.126721i
$638$	−3.12371	+	17.7154i	−0.123669	+	0.701360i
$639$		0			0
$640$	0.438421	+	2.48641i	0.0173301	+	0.0982839i
$641$	−50.1806	−	5.86527i	−1.98201	−	0.231664i	−0.998784	−	0.0492934i	$-0.984303\pi$
$641$	−50.1806	−	5.86527i	−1.98201	−	0.231664i	−0.983230	−	0.182371i	$-0.941623\pi$
$642$		0			0
$643$	−10.4349	+	11.0603i	−0.411510	+	0.436176i	−0.899665	−	0.436582i	$-0.856189\pi$
$643$	−10.4349	+	11.0603i	−0.411510	+	0.436176i	0.488154	+	0.872757i	$0.337670\pi$
$644$	−4.63353	+	10.7417i	−0.182586	+	0.423283i
$645$		0			0
$646$	49.3137	−	32.4341i	1.94022	−	1.27610i
$647$	8.72115			0.342864			0.171432	−	0.985196i	$-0.445161\pi$
$647$	8.72115			0.342864			0.171432	+	0.985196i	$0.445161\pi$
$648$		0			0
$649$	−3.48769			−0.136904
$650$	25.9451	−	17.0644i	1.01765	−	0.669320i
$651$		0			0
$652$	−2.99813	+	6.95045i	−0.117416	+	0.272201i
$653$	−9.43090	+	9.99617i	−0.369060	+	0.391180i	−0.885113	−	0.465376i	$-0.845919\pi$
$653$	−9.43090	+	9.99617i	−0.369060	+	0.391180i	0.516053	+	0.856556i	$0.327401\pi$
$654$		0			0
$655$	2.69224	+	0.314677i	0.105194	+	0.0122955i
$656$	6.01191	+	34.0952i	0.234726	+	1.33120i
$657$		0			0
$658$	−6.44283	+	36.5391i	−0.251168	+	1.42444i
$659$	12.4986	−	41.7482i	0.486877	−	1.62628i	−0.263066	−	0.964778i	$-0.584734\pi$
$659$	12.4986	−	41.7482i	0.486877	−	1.62628i	0.749943	−	0.661503i	$-0.230081\pi$
$660$		0			0
$661$	−1.75028	+	30.0511i	−0.0680778	+	1.16885i	0.775323	+	0.631566i	$0.217587\pi$
$661$	−1.75028	+	30.0511i	−0.0680778	+	1.16885i	−0.843400	+	0.537286i	$0.819450\pi$
$662$	15.9127	−	7.99167i	0.618466	−	0.310605i
$663$		0			0
$664$	0.911625	+	0.966266i	0.0353779	+	0.0374984i
$665$	−59.3752	+	21.6108i	−2.30247	+	0.838031i
$666$		0			0
$667$	10.6433	+	3.87386i	0.412112	+	0.149996i
$668$	0.236087	+	0.547312i	0.00913450	+	0.0211761i
$669$		0			0
$670$	4.07550	+	13.6131i	0.157450	+	0.525920i
$671$	21.1656	−	2.47391i	0.817090	−	0.0955041i
$672$		0			0
$673$	−1.29784	−	22.2830i	−0.0500279	−	0.858947i	−0.926220	−	0.376984i	$-0.876961\pi$
$673$	−1.29784	−	22.2830i	−0.0500279	−	0.858947i	0.876192	−	0.481963i	$-0.160076\pi$
$674$	−26.7669	−	46.3617i	−1.03102	−	1.78579i
$675$		0			0
$676$	8.66621	−	15.0103i	0.333316	−	0.577320i
$677$	−29.8861	−	15.0094i	−1.14862	−	0.576857i	−0.230463	−	0.973081i	$-0.574024\pi$
$677$	−29.8861	−	15.0094i	−1.14862	−	0.576857i	−0.918154	+	0.396224i	$0.870320\pi$
$678$		0			0
$679$	−23.1483	−	31.0936i	−0.888351	−	1.19326i
$680$	−1.46235	−	0.346583i	−0.0560786	−	0.0132909i
$681$		0			0
$682$	1.70891	−	2.29546i	0.0654374	−	0.0878976i
$683$	−0.481958	+	0.404411i	−0.0184416	+	0.0154744i	−0.651962	−	0.758252i	$-0.726054\pi$
$683$	−0.481958	+	0.404411i	−0.0184416	+	0.0154744i	0.633520	+	0.773726i	$0.281609\pi$
$684$		0			0
$685$	−8.55791	−	7.18094i	−0.326981	−	0.274370i
$686$	31.1094	−	7.37306i	1.18776	−	0.281505i
$687$		0			0
$688$	−14.4205	−	9.48452i	−0.549777	−	0.361594i
$689$	−14.9249	−	9.81625i	−0.568592	−	0.373969i
$690$		0			0
$691$	43.0099	−	10.1935i	1.63617	−	0.387780i	0.693225	−	0.720721i	$-0.256189\pi$
$691$	43.0099	−	10.1935i	1.63617	−	0.387780i	0.942948	+	0.332941i	$0.108041\pi$
$692$	−8.65033	−	7.25849i	−0.328836	−	0.275926i
$693$		0			0
$694$	20.2627	−	17.0024i	0.769160	−	0.645402i
$695$	44.9851	−	60.4254i	1.70638	−	2.29207i
$696$		0			0
$697$	−41.0357	−	9.72564i	−1.55434	−	0.368385i
$698$	−0.790266	−	1.06151i	−0.0299120	−	0.0401788i
$699$		0			0
$700$	38.8341	+	19.5032i	1.46779	+	0.737152i
$701$	21.3576	−	36.9925i	0.806667	−	1.39719i	−0.108493	−	0.994097i	$-0.534602\pi$
$701$	21.3576	−	36.9925i	0.806667	−	1.39719i	0.915160	−	0.403091i	$-0.132064\pi$
$702$		0			0
$703$	−10.5091	−	18.2023i	−0.396359	−	0.686515i
$704$	0.749688	+	12.8716i	0.0282549	+	0.485119i
$705$		0			0
$706$	24.9931	−	2.92128i	0.940628	−	0.109944i
$707$	3.54770	+	11.8501i	0.133425	+	0.445671i
$708$		0			0
$709$	−0.122138	−	0.283147i	−0.00458698	−	0.0106338i	0.915907	−	0.401390i	$-0.131473\pi$
$709$	−0.122138	−	0.283147i	−0.00458698	−	0.0106338i	−0.920494	+	0.390756i	$0.872214\pi$
$710$	1.60881	+	0.585560i	0.0603777	+	0.0219757i
$711$		0			0
$712$	0.878190	−	0.319635i	0.0329116	−	0.0119788i
$713$	−1.23651	−	1.31062i	−0.0463076	−	0.0490832i
$714$		0			0
$715$	10.2706	−	5.15810i	0.384099	−	0.192902i
$716$	1.60277	−	27.5185i	0.0598984	−	1.02842i
$717$		0			0
$718$	−10.1317	+	33.8422i	−0.378111	+	1.26298i
$719$	1.29284	−	7.33207i	0.0482149	−	0.273440i	−0.951164	−	0.308687i	$-0.900111\pi$
$719$	1.29284	−	7.33207i	0.0482149	−	0.273440i	0.999379	+	0.0352465i	$0.0112216\pi$
$720$		0			0
$721$	−3.00967	−	17.0687i	−0.112086	−	0.635671i
$722$	37.9563	+	4.43645i	1.41259	+	0.165108i
$723$		0			0
$724$	35.2873	−	37.4024i	1.31144	−	1.39005i
$725$	16.6648	−	38.6333i	0.618914	−	1.43480i
$726$		0			0
$727$	24.5837	−	16.1690i	0.911759	−	0.599674i	−0.00461790	−	0.999989i	$-0.501470\pi$
$727$	24.5837	−	16.1690i	0.911759	−	0.599674i	0.916377	+	0.400316i	$0.131100\pi$
$728$	−0.561349			−0.0208050
$729$		0			0
$730$	32.6906			1.20993
$731$	17.5658	−	11.5532i	0.649694	−	0.427311i
$732$		0			0
$733$	12.4469	−	28.8552i	0.459738	−	1.06579i	−0.517890	−	0.855447i	$-0.673282\pi$
$733$	12.4469	−	28.8552i	0.459738	−	1.06579i	0.977627	−	0.210344i	$-0.0674585\pi$
$734$	45.0329	−	47.7321i	1.66219	−	1.76182i
$735$		0			0
$736$	15.6076	+	1.82426i	0.575303	+	0.0672433i
$737$	0.540787	+	3.06696i	0.0199201	+	0.112973i
$738$		0			0
$739$	7.41959	−	42.0786i	0.272934	−	1.54788i	−0.472515	−	0.881322i	$-0.656654\pi$
$739$	7.41959	−	42.0786i	0.272934	−	1.54788i	0.745449	−	0.666562i	$-0.232235\pi$
$740$	−7.00129	+	23.3859i	−0.257373	+	0.859684i
$741$		0			0
$742$	2.87517	−	49.3647i	0.105551	−	1.81224i
$743$	−16.5797	+	8.32664i	−0.608250	+	0.305475i	−0.726135	−	0.687553i	$-0.758685\pi$
$743$	−16.5797	+	8.32664i	−0.608250	+	0.305475i	0.117884	+	0.993027i	$0.462389\pi$
$744$		0			0
$745$	−28.4978	−	30.2059i	−1.04408	−	1.10666i
$746$	3.82863	−	1.39351i	0.140176	−	0.0510200i
$747$		0			0
$748$	−14.1179	−	5.13849i	−0.516201	−	0.187882i
$749$	0.958465	+	2.22197i	0.0350215	+	0.0811890i
$750$		0			0
$751$	−14.8165	−	49.4907i	−0.540663	−	1.80594i	−0.590314	−	0.807174i	$-0.700996\pi$
$751$	−14.8165	−	49.4907i	−0.540663	−	1.80594i	0.0496513	−	0.998767i	$-0.484189\pi$
$752$	24.4636	−	2.85938i	0.892094	−	0.104271i
$753$		0			0
$754$	1.44150	+	24.7495i	0.0524962	+	0.901325i
$755$	28.7102	+	49.7275i	1.04487	+	1.80977i
$756$		0			0
$757$	12.7480	−	22.0801i	0.463333	−	0.802517i	−0.535791	−	0.844350i	$-0.679987\pi$
$757$	12.7480	−	22.0801i	0.463333	−	0.802517i	0.999125	+	0.0418338i	$0.0133200\pi$
$758$	−12.2877	−	6.17114i	−0.446311	−	0.224146i
$759$		0			0
$760$	−1.16206	−	1.56092i	−0.0421523	−	0.0566204i
$761$	12.1330	+	2.87557i	0.439820	+	0.104239i	0.444559	−	0.895750i	$-0.353360\pi$
$761$	12.1330	+	2.87557i	0.439820	+	0.104239i	−0.00473924	+	0.999989i	$0.501509\pi$
$762$		0			0
$763$	17.5988	−	23.6393i	0.637121	−	0.855802i
$764$	22.3474	−	18.7517i	0.808499	−	0.678411i
$765$		0			0
$766$	−6.65379	−	5.58319i	−0.240411	−	0.201729i
$767$	−4.67706	+	1.10848i	−0.168879	+	0.0400250i
$768$		0			0
$769$	−9.63904	−	6.33970i	−0.347593	−	0.228615i	0.363692	−	0.931519i	$-0.381516\pi$
$769$	−9.63904	−	6.33970i	−0.347593	−	0.228615i	−0.711285	+	0.702904i	$0.751886\pi$
$770$	26.5803	+	17.4821i	0.957886	+	0.630011i
$771$		0			0
$772$	5.70833	−	1.35290i	0.205447	−	0.0486919i
$773$	−2.68817	−	2.25564i	−0.0966866	−	0.0811297i	0.593163	−	0.805082i	$-0.297879\pi$
$773$	−2.68817	−	2.25564i	−0.0966866	−	0.0811297i	−0.689850	+	0.723953i	$0.742323\pi$
$774$		0			0
$775$	−5.12742	+	4.30242i	−0.184182	+	0.154547i
$776$	0.712916	−	0.957613i	0.0255922	−	0.0343763i
$777$		0			0
$778$	30.9163	+	7.32731i	1.10840	+	0.262697i
$779$	−32.6091	−	43.8016i	−1.16834	−	1.56936i
$780$		0			0
$781$	0.335303	+	0.168396i	0.0119981	+	0.00602567i
$782$	−9.35597	+	16.2050i	−0.334569	+	0.579490i
$783$		0

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)

\(f(q)\)	\(=\)	\(q+(1.68031 - 1.10516i) q^{2} +(0.809915 - 1.87759i) q^{4} +(-2.40279 + 2.54681i) q^{5} +(-2.90760 - 0.339850i) q^{7} +(-0.0156557 - 0.0887876i) q^{8} +O(q^{10})\)	\(q+(1.68031 - 1.10516i) q^{2} +(0.809915 - 1.87759i) q^{4} +(-2.40279 + 2.54681i) q^{5} +(-2.90760 - 0.339850i) q^{7} +(-0.0156557 - 0.0887876i) q^{8} +(-1.22281 + 6.93490i) q^{10} +(-0.442621 + 1.47846i) q^{11} +(-0.123669 + 2.12332i) q^{13} +(-5.26127 + 2.64231i) q^{14} +(2.68206 + 2.84282i) q^{16} +(-4.47367 + 1.62828i) q^{17} +(-5.79274 - 2.10839i) q^{19} +(2.83582 + 6.57416i) q^{20} +(0.890189 + 2.97344i) q^{22} +(1.94108 - 0.226880i) q^{23} +(-0.422110 - 7.24736i) q^{25} +(2.13880 + 3.70451i) q^{26} +(-2.99301 + 5.18405i) q^{28} +(5.17918 + 2.60108i) q^{29} +(-0.550579 - 0.739556i) q^{31} +(7.82392 + 1.85430i) q^{32} +(-5.71766 + 7.68015i) q^{34} +(7.85190 - 6.58853i) q^{35} +(2.61187 + 2.19162i) q^{37} +(-12.0637 + 2.85915i) q^{38} +(0.263742 + 0.173466i) q^{40} +(7.40100 + 4.86772i) q^{41} +(-4.29716 + 1.01845i) q^{43} +(2.41746 + 2.02849i) q^{44} +(3.01089 - 2.52643i) q^{46} +(3.76326 - 5.05493i) q^{47} +(1.52735 + 0.361989i) q^{49} +(-8.71876 - 11.7113i) q^{50} +(3.88657 + 1.95191i) q^{52} +(-4.19943 + 7.27362i) q^{53} +(-2.70182 - 4.67970i) q^{55} +(0.0153460 + 0.263480i) q^{56} +(11.5772 - 1.35319i) q^{58} +(0.648147 + 2.16496i) q^{59} +(-5.46905 - 12.6787i) q^{61} +(-1.74247 - 0.634208i) q^{62} +(7.85068 - 2.85741i) q^{64} +(-5.11053 - 5.41685i) q^{65} +(1.80329 - 0.905649i) q^{67} +(-0.566039 + 9.71852i) q^{68} +(5.91228 - 19.7484i) q^{70} +(0.0422183 - 0.239432i) q^{71} +(-0.806129 - 4.57178i) q^{73} +(6.81086 + 0.796075i) q^{74} +(-8.65032 + 9.16881i) q^{76} +(1.78942 - 4.14835i) q^{77} +(2.65633 - 1.74709i) q^{79} -13.6846 q^{80} +17.8156 q^{82} +(-12.3106 + 8.09679i) q^{83} +(6.60237 - 15.3060i) q^{85} +(-6.09503 + 6.46036i) q^{86} +(0.138198 + 0.0161531i) q^{88} +(1.80000 + 10.2083i) q^{89} +(1.08119 - 6.13174i) q^{91} +(1.14612 - 3.82832i) q^{92} +(0.736946 - 12.6529i) q^{94} +(19.2884 - 9.68700i) q^{95} +(9.08709 + 9.63176i) q^{97} +(2.96649 - 1.07971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 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 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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