LMFDB - Embedded newform 729.2.g.c.109.2

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			109.2
Character	$\chi$	$=$	729.109
Dual form			729.2.g.c.622.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07889 - 1.14356i) q^{2} +(-0.0274281 + 0.470923i) q^{4} +(-0.852512 + 0.0996444i) q^{5} +(2.97559 + 1.49440i) q^{7} +(-1.84059 + 1.54444i) q^{8} +O(q^{10})$	\(q+(-1.07889 - 1.14356i) q^{2} +(-0.0274281 + 0.470923i) q^{4} +(-0.852512 + 0.0996444i) q^{5} +(2.97559 + 1.49440i) q^{7} +(-1.84059 + 1.54444i) q^{8} +(1.03372 + 0.867390i) q^{10} +(0.146107 + 0.338713i) q^{11} +(-3.77713 - 0.895197i) q^{13} +(-1.50140 - 5.01504i) q^{14} +(4.68900 + 0.548065i) q^{16} +(-0.384378 + 2.17991i) q^{17} +(0.607044 + 3.44272i) q^{19} +(-0.0235420 - 0.404201i) q^{20} +(0.229704 - 0.532515i) q^{22} +(-7.28429 + 3.65831i) q^{23} +(-4.14838 + 0.983183i) q^{25} +(3.05140 + 5.28518i) q^{26} +(-0.785360 + 1.36028i) q^{28} +(-0.892472 + 2.98106i) q^{29} +(7.30581 + 4.80511i) q^{31} +(-1.56256 - 2.09889i) q^{32} +(2.90755 - 1.91233i) q^{34} +(-2.68563 - 0.977491i) q^{35} +(-6.17440 + 2.24730i) q^{37} +(3.28201 - 4.40850i) q^{38} +(1.41523 - 1.50006i) q^{40} +(2.19157 - 2.32293i) q^{41} +(-1.40273 + 1.88419i) q^{43} +(-0.163515 + 0.0595146i) q^{44} +(12.0424 + 4.38308i) q^{46} +(10.8880 - 7.16113i) q^{47} +(2.44079 + 3.27855i) q^{49} +(5.59996 + 3.68315i) q^{50} +(0.525168 - 1.75418i) q^{52} +(0.417342 - 0.722857i) q^{53} +(-0.158309 - 0.274198i) q^{55} +(-7.78483 + 1.84504i) q^{56} +(4.37189 - 2.19565i) q^{58} +(-2.21866 + 5.14344i) q^{59} +(0.489280 + 8.40062i) q^{61} +(-2.38725 - 13.5388i) q^{62} +(0.925198 - 5.24706i) q^{64} +(3.30926 + 0.386796i) q^{65} +(2.75718 + 9.20962i) q^{67} +(-1.01603 - 0.240803i) q^{68} +(1.77969 + 4.12577i) q^{70} +(11.0657 + 9.28524i) q^{71} +(5.24785 - 4.40347i) q^{73} +(9.23140 + 4.63618i) q^{74} +(-1.63790 + 0.191443i) q^{76} +(-0.0714187 + 1.22621i) q^{77} +(-10.1589 - 10.7678i) q^{79} -4.05204 q^{80} -5.02087 q^{82} +(1.03296 + 1.09488i) q^{83} +(0.110470 - 1.89670i) q^{85} +(3.66806 - 0.428735i) q^{86} +(-0.792043 - 0.397779i) q^{88} +(-3.47858 + 2.91888i) q^{89} +(-9.90141 - 8.30827i) q^{91} +(-1.52299 - 3.53068i) q^{92} +(-19.9361 - 4.72493i) q^{94} +(-0.860560 - 2.87447i) q^{95} +(-4.70641 - 0.550100i) q^{97} +(1.11586 - 6.32837i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.07889	−	1.14356i	−0.762890	−	0.808616i	0.223210	−	0.974770i	$-0.428346\pi$
$2$	−1.07889	−	1.14356i	−0.762890	−	0.808616i	−0.986100	+	0.166155i	$0.946865\pi$
$3$		0			0
$3$		0			0
$4$	−0.0274281	+	0.470923i	−0.0137141	+	0.235461i
$5$	−0.852512	+	0.0996444i	−0.381255	+	0.0445623i	−0.304562	−	0.952492i	$-0.598510\pi$
$5$	−0.852512	+	0.0996444i	−0.381255	+	0.0445623i	−0.0766929	+	0.997055i	$0.524436\pi$
$6$		0			0
$7$	2.97559	+	1.49440i	1.12467	+	0.564829i	0.911135	−	0.412108i	$-0.135207\pi$
$7$	2.97559	+	1.49440i	1.12467	+	0.564829i	0.213531	+	0.976936i	$0.431504\pi$
$8$	−1.84059	+	1.54444i	−0.650746	+	0.546041i
$9$		0			0
$10$	1.03372	+	0.867390i	0.326889	+	0.274293i
$11$	0.146107	+	0.338713i	0.0440528	+	0.102126i	0.938822	−	0.344404i	$-0.111919\pi$
$11$	0.146107	+	0.338713i	0.0440528	+	0.102126i	−0.894769	+	0.446530i	$0.852660\pi$
$12$		0			0
$13$	−3.77713	−	0.895197i	−1.04759	−	0.248283i	−0.329443	−	0.944176i	$-0.606861\pi$
$13$	−3.77713	−	0.895197i	−1.04759	−	0.248283i	−0.718146	+	0.695893i	$0.755009\pi$
$14$	−1.50140	−	5.01504i	−0.401267	−	1.34032i
$15$		0			0
$16$	4.68900	+	0.548065i	1.17225	+	0.137016i
$17$	−0.384378	+	2.17991i	−0.0932253	+	0.528707i	0.902051	+	0.431628i	$0.142061\pi$
$17$	−0.384378	+	2.17991i	−0.0932253	+	0.528707i	−0.995277	+	0.0970783i	$0.969050\pi$
$18$		0			0
$19$	0.607044	+	3.44272i	0.139265	+	0.789813i	0.971794	+	0.235831i	$0.0757813\pi$
$19$	0.607044	+	3.44272i	0.139265	+	0.789813i	−0.832529	+	0.553982i	$0.813108\pi$
$20$	−0.0235420	−	0.404201i	−0.00526415	−	0.0903820i
$21$		0			0
$22$	0.229704	−	0.532515i	0.0489732	−	0.113533i
$23$	−7.28429	+	3.65831i	−1.51888	+	0.762810i	−0.995979	−	0.0895845i	$-0.971446\pi$
$23$	−7.28429	+	3.65831i	−1.51888	+	0.762810i	−0.522900	+	0.852394i	$0.675150\pi$
$24$		0			0
$25$	−4.14838	+	0.983183i	−0.829675	+	0.196637i
$26$	3.05140	+	5.28518i	0.598429	+	1.03651i
$27$		0			0
$28$	−0.785360	+	1.36028i	−0.148419	+	0.257069i
$29$	−0.892472	+	2.98106i	−0.165728	+	0.553570i	0.834270	+	0.551357i	$0.185890\pi$
$29$	−0.892472	+	2.98106i	−0.165728	+	0.553570i	−0.999998	+	0.00221315i	$0.999296\pi$
$30$		0			0
$31$	7.30581	+	4.80511i	1.31216	+	0.863023i	0.996314	−	0.0857865i	$-0.0273403\pi$
$31$	7.30581	+	4.80511i	1.31216	+	0.863023i	0.315849	+	0.948809i	$0.397711\pi$
$32$	−1.56256	−	2.09889i	−0.276225	−	0.371034i
$33$		0			0
$34$	2.90755	−	1.91233i	0.498641	−	0.327962i
$35$	−2.68563	−	0.977491i	−0.453955	−	0.165226i
$36$		0			0
$37$	−6.17440	+	2.24730i	−1.01506	+	0.369453i	−0.795376	−	0.606117i	$-0.792726\pi$
$37$	−6.17440	+	2.24730i	−1.01506	+	0.369453i	−0.219689	+	0.975570i	$0.570504\pi$
$38$	3.28201	−	4.40850i	0.532412	−	0.715153i
$39$		0			0
$40$	1.41523	−	1.50006i	0.223767	−	0.237180i
$41$	2.19157	−	2.32293i	0.342266	−	0.362781i	−0.533260	−	0.845951i	$-0.679033\pi$
$41$	2.19157	−	2.32293i	0.342266	−	0.362781i	0.875526	+	0.483170i	$0.160515\pi$
$42$		0			0
$43$	−1.40273	+	1.88419i	−0.213914	+	0.287336i	−0.896109	−	0.443834i	$-0.853618\pi$
$43$	−1.40273	+	1.88419i	−0.213914	+	0.287336i	0.682195	+	0.731170i	$0.261025\pi$
$44$	−0.163515	+	0.0595146i	−0.0246508	+	0.00897217i
$45$		0			0
$46$	12.0424	+	4.38308i	1.77556	+	0.646250i
$47$	10.8880	−	7.16113i	1.58817	−	1.04456i	0.623252	−	0.782021i	$-0.285811\pi$
$47$	10.8880	−	7.16113i	1.58817	−	1.04456i	0.964922	−	0.262537i	$-0.0845593\pi$
$48$		0			0
$49$	2.44079	+	3.27855i	0.348684	+	0.468364i
$50$	5.59996	+	3.68315i	0.791954	+	0.520876i
$51$		0			0
$52$	0.525168	−	1.75418i	0.0728278	−	0.243262i
$53$	0.417342	−	0.722857i	0.0573263	−	0.0992920i	−0.835938	−	0.548824i	$-0.815076\pi$
$53$	0.417342	−	0.722857i	0.0573263	−	0.0992920i	0.893264	+	0.449532i	$0.148409\pi$
$54$		0			0
$55$	−0.158309	−	0.274198i	−0.0213463	−	0.0369729i
$56$	−7.78483	+	1.84504i	−1.04029	+	0.246554i
$57$		0			0
$58$	4.37189	−	2.19565i	0.574058	−	0.288303i
$59$	−2.21866	+	5.14344i	−0.288845	+	0.669619i	−0.999422	−	0.0340010i	$-0.989175\pi$
$59$	−2.21866	+	5.14344i	−0.288845	+	0.669619i	0.710576	+	0.703620i	$0.248434\pi$
$60$		0			0
$61$	0.489280	+	8.40062i	0.0626459	+	1.07559i	0.872391	+	0.488808i	$0.162568\pi$
$61$	0.489280	+	8.40062i	0.0626459	+	1.07559i	−0.809745	+	0.586781i	$0.800395\pi$
$62$	−2.38725	−	13.5388i	−0.303181	−	1.71943i
$63$		0			0
$64$	0.925198	−	5.24706i	0.115650	−	0.655882i
$65$	3.30926	+	0.386796i	0.410463	+	0.0479762i
$66$		0			0
$67$	2.75718	+	9.20962i	0.336843	+	1.12513i	0.943832	+	0.330425i	$0.107192\pi$
$67$	2.75718	+	9.20962i	0.336843	+	1.12513i	−0.606989	+	0.794710i	$0.707623\pi$
$68$	−1.01603	−	0.240803i	−0.123212	−	0.0292017i
$69$		0			0
$70$	1.77969	+	4.12577i	0.212713	+	0.493124i
$71$	11.0657	+	9.28524i	1.31326	+	1.10196i	0.987688	+	0.156438i	$0.0500011\pi$
$71$	11.0657	+	9.28524i	1.31326	+	1.10196i	0.325571	+	0.945517i	$0.394443\pi$
$72$		0			0
$73$	5.24785	−	4.40347i	0.614214	−	0.515387i	−0.281765	−	0.959484i	$-0.590920\pi$
$73$	5.24785	−	4.40347i	0.614214	−	0.515387i	0.895979	+	0.444097i	$0.146475\pi$
$74$	9.23140	+	4.63618i	1.07313	+	0.538945i
$75$		0			0
$76$	−1.63790	+	0.191443i	−0.187880	+	0.0219601i
$77$	−0.0714187	+	1.22621i	−0.00813891	+	0.139740i
$78$		0			0
$79$	−10.1589	−	10.7678i	−1.14296	−	1.21147i	−0.974170	−	0.225817i	$-0.927495\pi$
$79$	−10.1589	−	10.7678i	−1.14296	−	1.21147i	−0.168792	−	0.985652i	$-0.553987\pi$
$80$	−4.05204			−0.453032
$81$		0			0
$82$	−5.02087			−0.554462
$83$	1.03296	+	1.09488i	0.113382	+	0.120178i	0.781579	−	0.623807i	$-0.214415\pi$
$83$	1.03296	+	1.09488i	0.113382	+	0.120178i	−0.668196	+	0.743985i	$0.732933\pi$
$84$		0			0
$85$	0.110470	−	1.89670i	0.0119822	−	0.205727i
$86$	3.66806	−	0.428735i	0.395537	−	0.0462317i
$87$		0			0
$88$	−0.792043	−	0.397779i	−0.0844320	−	0.0424034i
$89$	−3.47858	+	2.91888i	−0.368729	+	0.309400i	−0.808259	−	0.588828i	$-0.799590\pi$
$89$	−3.47858	+	2.91888i	−0.368729	+	0.309400i	0.439530	+	0.898228i	$0.355145\pi$
$90$		0			0
$91$	−9.90141	−	8.30827i	−1.03795	−	0.870944i
$92$	−1.52299	−	3.53068i	−0.158782	−	0.368099i
$93$		0			0
$94$	−19.9361	−	4.72493i	−2.05625	−	0.487340i
$95$	−0.860560	−	2.87447i	−0.0882916	−	0.294914i
$96$		0			0
$97$	−4.70641	−	0.550100i	−0.477863	−	0.0558542i	−0.126248	−	0.991999i	$-0.540293\pi$
$97$	−4.70641	−	0.550100i	−0.477863	−	0.0558542i	−0.351616	+	0.936145i	$0.614368\pi$
$98$	1.11586	−	6.32837i	0.112719	−	0.639262i
$99$		0			0
$100$	−0.349221	−	1.98053i	−0.0349221	−	0.198053i
$101$	−0.0201885	−	0.346623i	−0.00200883	−	0.0344902i	0.997155	−	0.0753813i	$-0.0240174\pi$
$101$	−0.0201885	−	0.346623i	−0.00200883	−	0.0344902i	−0.999164	+	0.0408910i	$0.986980\pi$
$102$		0			0
$103$	3.34563	−	7.75604i	0.329654	−	0.764225i	−0.670104	−	0.742267i	$-0.733751\pi$
$103$	3.34563	−	7.75604i	0.329654	−	0.764225i	0.999759	−	0.0219581i	$-0.00699004\pi$
$104$	8.33472	−	4.18585i	0.817287	−	0.410457i
$105$		0			0
$106$	−1.27689	+	0.302629i	−0.124023	+	0.0293939i
$107$	8.01529	+	13.8829i	0.774868	+	1.34211i	0.934869	+	0.354993i	$0.115517\pi$
$107$	8.01529	+	13.8829i	0.774868	+	1.34211i	−0.160001	+	0.987117i	$0.551150\pi$
$108$		0			0
$109$	−2.57355	+	4.45751i	−0.246501	+	0.426952i	−0.962553	−	0.271095i	$-0.912614\pi$
$109$	−2.57355	+	4.45751i	−0.246501	+	0.426952i	0.716052	+	0.698047i	$0.245948\pi$
$110$	−0.142764	+	0.476864i	−0.0136120	+	0.0454672i
$111$		0			0
$112$	13.1335	+	8.63804i	1.24100	+	0.816218i
$113$	−1.91053	−	2.56629i	−0.179728	−	0.241417i	0.703125	−	0.711066i	$-0.251788\pi$
$113$	−1.91053	−	2.56629i	−0.179728	−	0.241417i	−0.882853	+	0.469650i	$0.844380\pi$
$114$		0			0
$115$	5.84542	−	3.84459i	0.545088	−	0.358510i
$116$	−1.37937	−	0.502050i	−0.128072	−	0.0466142i
$117$		0			0
$118$	8.27550	−	3.01204i	0.761822	−	0.277281i
$119$	−4.40140	+	5.91211i	−0.403476	+	0.541962i
$120$		0			0
$121$	7.45528	−	7.90213i	0.677753	−	0.718376i
$122$	9.07870	−	9.62286i	0.821947	−	0.871213i
$123$		0			0
$124$	−2.46322	+	3.30868i	−0.221204	+	0.297128i
$125$	7.47134	−	2.71935i	0.668257	−	0.243226i
$126$		0			0
$127$	−4.34690	−	1.58214i	−0.385725	−	0.140392i	0.141877	−	0.989884i	$-0.454686\pi$
$127$	−4.34690	−	1.58214i	−0.385725	−	0.140392i	−0.527601	+	0.849492i	$0.676909\pi$
$128$	−11.3709	+	7.47874i	−1.00505	+	0.661033i
$129$		0			0
$130$	−3.12800	−	4.20163i	−0.274343	−	0.368507i
$131$	2.09407	+	1.37729i	0.182960	+	0.120335i	0.637685	−	0.770297i	$-0.279892\pi$
$131$	2.09407	+	1.37729i	0.182960	+	0.120335i	−0.454725	+	0.890632i	$0.650262\pi$
$132$		0			0
$133$	−3.33847	+	11.1513i	−0.289482	+	0.966938i
$134$	7.55703	−	13.0892i	0.652828	−	1.13073i
$135$		0			0
$136$	−2.65926	−	4.60597i	−0.228029	−	0.394959i
$137$	−9.33406	+	2.21221i	−0.797462	+	0.189002i	−0.609096	−	0.793097i	$-0.708467\pi$
$137$	−9.33406	+	2.21221i	−0.797462	+	0.189002i	−0.188367	+	0.982099i	$0.560319\pi$
$138$		0			0
$139$	−17.8753	+	8.97732i	−1.51616	+	0.761446i	−0.995717	−	0.0924483i	$-0.970531\pi$
$139$	−17.8753	+	8.97732i	−1.51616	+	0.761446i	−0.520446	+	0.853894i	$0.674234\pi$
$140$	0.533984	−	1.23791i	0.0451299	−	0.104623i
$141$		0			0
$142$	−1.32049	−	22.6720i	−0.110813	−	1.90259i
$143$	−0.248649	−	1.41016i	−0.0207931	−	0.117923i
$144$		0			0
$145$	0.463797	−	2.63032i	0.0385163	−	0.218437i
$146$	−10.6975	−	1.25035i	−0.885328	−	0.103480i
$147$		0			0
$148$	−0.888951	−	2.96930i	−0.0730713	−	0.244075i
$149$	11.1322	+	2.63838i	0.911986	+	0.216145i	0.659718	−	0.751513i	$-0.270676\pi$
$149$	11.1322	+	2.63838i	0.911986	+	0.216145i	0.252267	+	0.967658i	$0.418824\pi$
$150$		0			0
$151$	1.45308	+	3.36861i	0.118250	+	0.274134i	0.967053	−	0.254575i	$-0.0819356\pi$
$151$	1.45308	+	3.36861i	0.118250	+	0.274134i	−0.848803	+	0.528709i	$0.822676\pi$
$152$	−6.43437	−	5.39908i	−0.521897	−	0.437923i
$153$		0			0
$154$	1.47929	−	1.24127i	0.119205	−	0.100025i
$155$	−6.70710	−	3.36843i	−0.538727	−	0.270559i
$156$		0			0
$157$	−7.74028	+	0.904710i	−0.617742	+	0.0722037i	−0.419208	−	0.907890i	$-0.637692\pi$
$157$	−7.74028	+	0.904710i	−0.617742	+	0.0722037i	−0.198534	+	0.980094i	$0.563618\pi$
$158$	−1.35325	+	23.2345i	−0.107659	+	1.84843i
$159$		0			0
$160$	1.54125	+	1.63363i	0.121846	+	0.129149i
$161$	−27.1420			−2.13909
$162$		0			0
$163$	−6.86435			−0.537657			−0.268829	−	0.963188i	$-0.586637\pi$
$163$	−6.86435			−0.537657			−0.268829	+	0.963188i	$0.586637\pi$
$164$	1.03381	+	1.09578i	0.0807270	+	0.0855657i
$165$		0			0
$166$	0.137600	−	2.36250i	0.0106798	−	0.183366i
$167$	−17.8511	+	2.08649i	−1.38136	+	0.161458i	−0.774109	−	0.633053i	$-0.781802\pi$
$167$	−17.8511	+	2.08649i	−1.38136	+	0.161458i	−0.607250	+	0.794511i	$0.707728\pi$
$168$		0			0
$169$	1.84814	+	0.928172i	0.142165	+	0.0713978i
$170$	−2.28817	+	1.92000i	−0.175495	+	0.147258i
$171$		0			0
$172$	−0.848833	−	0.712256i	−0.0647229	−	0.0543090i
$173$	−4.50040	−	10.4331i	−0.342159	−	0.793213i	−0.999224	−	0.0393799i	$-0.987462\pi$
$173$	−4.50040	−	10.4331i	−0.342159	−	0.793213i	0.657065	−	0.753834i	$-0.271798\pi$
$174$		0			0
$175$	−13.8131	−	3.27377i	−1.04417	−	0.247474i
$176$	0.499457	+	1.66830i	0.0376480	+	0.125753i
$177$		0			0
$178$	7.09090	+	0.828808i	0.531486	+	0.0621218i
$179$	3.90136	−	22.1257i	0.291601	−	1.65375i	−0.389102	−	0.921194i	$-0.627215\pi$
$179$	3.90136	−	22.1257i	0.291601	−	1.65375i	0.680704	−	0.732559i	$-0.261674\pi$
$180$		0			0
$181$	0.281757	+	1.59792i	0.0209428	+	0.118773i	0.993487	−	0.113946i	$-0.0363490\pi$
$181$	0.281757	+	1.59792i	0.0209428	+	0.118773i	−0.972544	+	0.232718i	$0.925238\pi$
$182$	1.18156	+	20.2865i	0.0875827	+	1.50374i
$183$		0			0
$184$	7.75735	−	17.9835i	0.571879	−	1.32576i
$185$	5.03982	−	2.53109i	0.370535	−	0.186090i
$186$		0			0
$187$	−0.794526	+	0.188306i	−0.0581015	+	0.0137703i
$188$	3.07370	+	5.32381i	0.224173	+	0.388279i
$189$		0			0
$190$	−2.35867	+	4.08533i	−0.171116	+	0.296381i
$191$	−1.04911	+	3.50427i	−0.0759110	+	0.253560i	−0.987519	−	0.157500i	$-0.949656\pi$
$191$	−1.04911	+	3.50427i	−0.0759110	+	0.253560i	0.911608	+	0.411061i	$0.134842\pi$
$192$		0			0
$193$	−18.0937	−	11.9004i	−1.30241	−	0.856611i	−0.306948	−	0.951726i	$-0.599308\pi$
$193$	−18.0937	−	11.9004i	−1.30241	−	0.856611i	−0.995466	+	0.0951151i	$0.969678\pi$
$194$	4.44862	+	5.97554i	0.319392	+	0.429019i
$195$		0			0
$196$	−1.61089	+	1.05950i	−0.115064	+	0.0756785i
$197$	3.46682	+	1.26182i	0.247001	+	0.0899010i	0.462554	−	0.886591i	$-0.346933\pi$
$197$	3.46682	+	1.26182i	0.247001	+	0.0899010i	−0.215553	+	0.976492i	$0.569155\pi$
$198$		0			0
$199$	1.25063	−	0.455191i	0.0886546	−	0.0322676i	−0.297312	−	0.954780i	$-0.596090\pi$
$199$	1.25063	−	0.455191i	0.0886546	−	0.0322676i	0.385967	+	0.922513i	$0.373868\pi$
$200$	6.11698	−	8.21654i	0.432536	−	0.580997i
$201$		0			0
$202$	−0.374601	+	0.397054i	−0.0263568	+	0.0279366i
$203$	−7.11052	+	7.53671i	−0.499061	+	0.528973i
$204$		0			0
$205$	−1.63688	+	2.19871i	−0.114324	+	0.153564i
$206$	−12.4790	+	4.54199i	−0.869454	+	0.316456i
$207$		0			0
$208$	−17.2204	−	6.26770i	−1.19402	−	0.434587i
$209$	−1.07740	+	0.708617i	−0.0745253	+	0.0490161i
$210$		0			0
$211$	−2.82054	−	3.78864i	−0.194174	−	0.260821i	0.694364	−	0.719624i	$-0.255686\pi$
$211$	−2.82054	−	3.78864i	−0.194174	−	0.260821i	−0.888538	+	0.458803i	$0.848278\pi$
$212$	0.328963	+	0.216362i	0.0225933	+	0.0148598i
$213$		0			0
$214$	7.22825	−	24.1440i	0.494113	−	1.65045i
$215$	1.00809	−	1.74607i	0.0687514	−	0.119081i
$216$		0			0
$217$	14.5583	+	25.2158i	0.988285	+	1.71176i
$218$	7.87398	−	1.86617i	0.533294	−	0.126393i
$219$		0			0
$220$	0.133468	−	0.0670303i	0.00899844	−	0.00451918i
$221$	3.40330	−	7.88973i	0.228931	−	0.530721i
$222$		0			0
$223$	−0.175101	−	3.00636i	−0.0117256	−	0.201321i	−0.999083	−	0.0428119i	$-0.986368\pi$
$223$	−0.175101	−	3.00636i	−0.0117256	−	0.201321i	0.987358	−	0.158509i	$-0.0506687\pi$
$224$	−1.51297	−	8.58050i	−0.101090	−	0.573309i
$225$		0			0
$226$	−0.873444	+	4.95355i	−0.0581006	+	0.329505i
$227$	−1.93582	−	0.226265i	−0.128485	−	0.0150177i	0.0516073	−	0.998667i	$-0.483566\pi$
$227$	−1.93582	−	0.226265i	−0.128485	−	0.0150177i	−0.180092	+	0.983650i	$0.557640\pi$
$228$		0			0
$229$	8.12873	+	27.1519i	0.537162	+	1.79425i	0.604609	+	0.796522i	$0.293329\pi$
$229$	8.12873	+	27.1519i	0.537162	+	1.79425i	−0.0674471	+	0.997723i	$0.521485\pi$
$230$	−10.7031	−	2.53667i	−0.705739	−	0.167263i
$231$		0			0
$232$	−2.96139	−	6.86528i	−0.194425	−	0.450727i
$233$	−1.21591	−	1.02027i	−0.0796571	−	0.0668402i	0.602090	−	0.798428i	$-0.294335\pi$
$233$	−1.21591	−	1.02027i	−0.0796571	−	0.0668402i	−0.681747	+	0.731588i	$0.738779\pi$
$234$		0			0
$235$	−8.56856	+	7.18988i	−0.558952	+	0.469016i
$236$	−2.36131	−	1.18589i	−0.153708	−	0.0771952i
$237$		0			0
$238$	11.5095	−	1.34526i	0.746047	−	0.0872004i
$239$	1.28265	−	22.0222i	0.0829676	−	1.42450i	−0.658031	−	0.752991i	$-0.728610\pi$
$239$	1.28265	−	22.0222i	0.0829676	−	1.42450i	0.740998	−	0.671507i	$-0.234353\pi$
$240$		0			0
$241$	4.63403	+	4.91178i	0.298504	+	0.316396i	0.859214	−	0.511617i	$-0.170953\pi$
$241$	4.63403	+	4.91178i	0.298504	+	0.316396i	−0.560710	+	0.828012i	$0.689472\pi$
$242$	−17.0799			−1.09794
$243$		0			0
$244$	−3.96946			−0.254119
$245$	−2.40749	−	2.55179i	−0.153809	−	0.163028i
$246$		0			0
$247$	0.789025	−	13.5470i	0.0502044	−	0.861977i
$248$	−20.8682	+	2.43914i	−1.32513	+	0.154885i
$249$		0			0
$250$	−11.1705	−	5.61002i	−0.706482	−	0.354809i
$251$	−7.86828	+	6.60227i	−0.496642	+	0.416732i	−0.856399	−	0.516314i	$-0.827304\pi$
$251$	−7.86828	+	6.60227i	−0.496642	+	0.416732i	0.359758	+	0.933046i	$0.382859\pi$
$252$		0			0
$253$	−2.30340	−	1.93278i	−0.144813	−	0.121513i
$254$	2.88055	+	6.67787i	0.180742	+	0.419007i
$255$		0			0
$256$	10.4515	+	2.47705i	0.653218	+	0.154815i
$257$	6.96201	+	23.2547i	0.434278	+	1.45059i	0.842991	+	0.537927i	$0.180792\pi$
$257$	6.96201	+	23.2547i	0.434278	+	1.45059i	−0.408713	+	0.912663i	$0.634022\pi$
$258$		0			0
$259$	−21.7308	−	2.53997i	−1.35029	−	0.157826i
$260$	−0.272918	+	1.54779i	−0.0169257	+	0.0959901i
$261$		0			0
$262$	−0.684261	−	3.88064i	−0.0422738	−	0.239746i
$263$	−0.844614	−	14.5015i	−0.0520811	−	0.894198i	−0.918633	−	0.395111i	$-0.870706\pi$
$263$	−0.844614	−	14.5015i	−0.0520811	−	0.894198i	0.866552	−	0.499087i	$-0.166331\pi$
$264$		0			0
$265$	−0.283760	+	0.657830i	−0.0174313	+	0.0404102i
$266$	16.3539	−	8.21325i	1.00272	−	0.503587i
$267$		0			0
$268$	−4.41265	+	1.04582i	−0.269545	+	0.0638834i
$269$	5.88635	+	10.1955i	0.358897	+	0.621628i	0.987777	−	0.155874i	$-0.0498195\pi$
$269$	5.88635	+	10.1955i	0.358897	+	0.621628i	−0.628880	+	0.777503i	$0.716486\pi$
$270$		0			0
$271$	2.10182	−	3.64046i	0.127677	−	0.221142i	−0.795099	−	0.606479i	$-0.792581\pi$
$271$	2.10182	−	3.64046i	0.127677	−	0.221142i	0.922776	+	0.385337i	$0.125915\pi$
$272$	−2.99708	+	10.0110i	−0.181725	+	0.607003i
$273$		0			0
$274$	12.6002	+	8.28728i	0.761206	+	0.500653i
$275$	−0.939122	−	1.26146i	−0.0566312	−	0.0760689i
$276$		0			0
$277$	5.36017	−	3.52544i	0.322061	−	0.211823i	−0.378175	−	0.925734i	$-0.623448\pi$
$277$	5.36017	−	3.52544i	0.322061	−	0.211823i	0.700236	+	0.713911i	$0.253078\pi$
$278$	29.5515	+	10.7559i	1.77238	+	0.645095i
$279$		0			0
$280$	6.45281	−	2.34863i	0.385629	−	0.140358i
$281$	1.21369	−	1.63027i	0.0724028	−	0.0972539i	−0.764446	−	0.644687i	$-0.776988\pi$
$281$	1.21369	−	1.63027i	0.0724028	−	0.0972539i	0.836849	+	0.547433i	$0.184395\pi$
$282$		0			0
$283$	5.11762	−	5.42436i	0.304211	−	0.322445i	−0.557176	−	0.830395i	$-0.688115\pi$
$283$	5.11762	−	5.42436i	0.304211	−	0.322445i	0.861387	+	0.507950i	$0.169596\pi$
$284$	−4.67614	+	4.95642i	−0.277478	+	0.294110i
$285$		0			0
$286$	−1.34433	+	1.80575i	−0.0794919	+	0.106776i
$287$	9.99260	−	3.63701i	0.589844	−	0.214686i
$288$		0			0
$289$	11.3705	+	4.13852i	0.668853	+	0.243442i
$290$	−3.50831	+	2.30745i	−0.206015	+	0.135498i
$291$		0			0
$292$	1.92975	+	2.59211i	0.112930	+	0.151692i
$293$	−18.3030	−	12.0381i	−1.06927	−	0.703271i	−0.112365	−	0.993667i	$-0.535843\pi$
$293$	−18.3030	−	12.0381i	−1.06927	−	0.703271i	−0.956907	+	0.290396i	$0.906213\pi$
$294$		0			0
$295$	1.37892	−	4.60593i	0.0802840	−	0.268167i
$296$	7.89371	−	13.6723i	0.458812	−	0.794687i
$297$		0			0
$298$	−8.99328	−	15.5768i	−0.520967	−	0.902341i
$299$	30.7886	−	7.29704i	1.78055	−	0.421999i
$300$		0			0
$301$	−6.98966	+	3.51034i	−0.402877	+	0.202333i
$302$	2.28449	−	5.29604i	0.131457	−	0.304753i
$303$		0			0
$304$	0.959594	+	16.4756i	0.0550365	+	0.944940i
$305$	−1.25419	−	7.11288i	−0.0718149	−	0.407282i
$306$		0			0
$307$	0.875956	−	4.96780i	0.0499935	−	0.283527i	−0.949554	−	0.313603i	$-0.898464\pi$
$307$	0.875956	−	4.96780i	0.0499935	−	0.283527i	0.999548	+	0.0300761i	$0.00957496\pi$
$308$	−0.575492	−	0.0672654i	−0.0327917	−	0.00383280i
$309$		0			0
$310$	3.38423	+	11.3041i	0.192211	+	0.642030i
$311$	4.65636	+	1.10358i	0.264038	+	0.0625782i	0.360502	−	0.932758i	$-0.382605\pi$
$311$	4.65636	+	1.10358i	0.264038	+	0.0625782i	−0.0964644	+	0.995336i	$0.530753\pi$
$312$		0			0
$313$	5.72173	+	13.2645i	0.323411	+	0.749752i	0.999911	+	0.0133092i	$0.00423657\pi$
$313$	5.72173	+	13.2645i	0.323411	+	0.749752i	−0.676500	+	0.736443i	$0.736504\pi$
$314$	9.38549	+	7.87536i	0.529654	+	0.444433i
$315$		0			0
$316$	5.34943	−	4.48870i	0.300929	−	0.252509i
$317$	8.60906	+	4.32363i	0.483533	+	0.242839i	0.673829	−	0.738887i	$-0.264648\pi$
$317$	8.60906	+	4.32363i	0.483533	+	0.242839i	−0.190296	+	0.981727i	$0.560945\pi$
$318$		0			0
$319$	−1.14012	+	0.133261i	−0.0638346	+	0.00746119i
$320$	−0.265903	+	4.56537i	−0.0148644	+	0.255212i
$321$		0			0
$322$	29.2832	+	31.0384i	1.63189	+	1.72970i
$323$	−7.73816			−0.430563
$324$		0			0
$325$	16.5491			0.917980
$326$	7.40587	+	7.84976i	0.410173	+	0.434758i
$327$		0			0
$328$	−0.446162	+	7.66030i	−0.0246352	+	0.422969i
$329$	43.0997	−	5.03763i	2.37616	−	0.277733i
$330$		0			0
$331$	9.47900	+	4.76053i	0.521013	+	0.261663i	0.689813	−	0.723988i	$-0.257693\pi$
$331$	9.47900	+	4.76053i	0.521013	+	0.261663i	−0.168800	+	0.985650i	$0.553989\pi$
$332$	−0.543935	+	0.456416i	−0.0298523	+	0.0250491i
$333$		0			0
$334$	21.6454	+	18.1626i	1.18438	+	0.993814i
$335$	−3.26822	−	7.57658i	−0.178562	−	0.413953i
$336$		0			0
$337$	22.9186	+	5.43181i	1.24846	+	0.295889i	0.801135	−	0.598484i	$-0.204230\pi$
$337$	22.9186	+	5.43181i	1.24846	+	0.295889i	0.447321	+	0.894373i	$0.352378\pi$
$338$	−0.932524	−	3.11485i	−0.0507226	−	0.169425i
$339$		0			0
$340$	0.890171	+	0.104046i	0.0482763	+	0.00564269i
$341$	−0.560126	+	3.17663i	−0.0303325	+	0.172024i
$342$		0			0
$343$	−1.68412	−	9.55114i	−0.0909341	−	0.515713i
$344$	−0.328168	−	5.63444i	−0.0176937	−	0.303788i
$345$		0			0
$346$	−7.07539	+	16.4026i	−0.380375	+	0.881809i
$347$	−12.9825	+	6.52006i	−0.696938	+	0.350015i	−0.761740	−	0.647883i	$-0.775655\pi$
$347$	−12.9825	+	6.52006i	−0.696938	+	0.350015i	0.0648023	+	0.997898i	$0.479358\pi$
$348$		0			0
$349$	25.9860	−	6.15879i	1.39100	−	0.329673i	0.534215	−	0.845349i	$-0.320607\pi$
$349$	25.9860	−	6.15879i	1.39100	−	0.329673i	0.856784	+	0.515676i	$0.172459\pi$
$350$	11.1591	+	19.3281i	0.596478	+	1.03313i
$351$		0			0
$352$	0.482619	−	0.835921i	0.0257237	−	0.0445548i
$353$	3.21627	−	10.7431i	0.171185	−	0.571797i	−0.828741	−	0.559632i	$-0.810943\pi$
$353$	3.21627	−	10.7431i	0.171185	−	0.571797i	0.999926	−	0.0121648i	$-0.00387227\pi$
$354$		0			0
$355$	−10.3589	−	6.81315i	−0.549793	−	0.361604i
$356$	−1.27915	−	1.71820i	−0.0677950	−	0.0910646i
$357$		0			0
$358$	−29.5111	+	19.4098i	−1.55971	+	1.02584i
$359$	25.7279	+	9.36419i	1.35787	+	0.494223i	0.915394	−	0.402559i	$-0.131879\pi$
$359$	25.7279	+	9.36419i	1.35787	+	0.494223i	0.442473	+	0.896782i	$0.354101\pi$
$360$		0			0
$361$	6.37036	−	2.31862i	0.335282	−	0.122033i
$362$	1.52333	−	2.04618i	0.0800643	−	0.107545i
$363$		0			0
$364$	4.18413	−	4.43492i	0.219308	−	0.232453i
$365$	−4.03507	+	4.27693i	−0.211205	+	0.223865i
$366$		0			0
$367$	1.89511	−	2.54558i	0.0989241	−	0.132878i	−0.749905	−	0.661546i	$-0.769901\pi$
$367$	1.89511	−	2.54558i	0.0989241	−	0.132878i	0.848829	+	0.528668i	$0.177308\pi$
$368$	−36.1610	+	13.1615i	−1.88502	+	0.686092i
$369$		0			0
$370$	−8.33185	−	3.03255i	−0.433152	−	0.157655i
$371$	2.32207	−	1.52725i	0.120556	−	0.0792909i
$372$		0			0
$373$	14.3282	+	19.2462i	0.741888	+	0.996529i	0.999541	+	0.0302912i	$0.00964347\pi$
$373$	14.3282	+	19.2462i	0.741888	+	0.996529i	−0.257653	+	0.966238i	$0.582949\pi$
$374$	1.07254	+	0.705423i	0.0554599	+	0.0364765i
$375$		0			0
$376$	−8.98035	+	29.9965i	−0.463126	+	1.54695i
$377$	6.03963	−	10.4609i	0.311057	−	0.538766i
$378$		0			0
$379$	−4.78175	−	8.28224i	−0.245622	−	0.425430i	0.716684	−	0.697398i	$-0.245659\pi$
$379$	−4.78175	−	8.28224i	−0.245622	−	0.425430i	−0.962306	+	0.271968i	$0.912326\pi$
$380$	1.37726	−	0.326416i	0.0706518	−	0.0167448i
$381$		0			0
$382$	5.13920	−	2.58101i	0.262945	−	0.132056i
$383$	−3.40102	+	7.88446i	−0.173784	+	0.402877i	−0.982740	−	0.184993i	$-0.940774\pi$
$383$	−3.40102	+	7.88446i	−0.173784	+	0.402877i	0.808956	+	0.587869i	$0.200033\pi$
$384$		0			0
$385$	−0.0612998	−	1.05248i	−0.00312413	−	0.0536392i
$386$	5.91232	+	33.5304i	0.300929	+	1.70665i
$387$		0			0
$388$	0.388143	−	2.20127i	0.0197050	−	0.111752i
$389$	14.3485	+	1.67710i	0.727498	+	0.0850323i	0.471776	−	0.881718i	$-0.343613\pi$
$389$	14.3485	+	1.67710i	0.727498	+	0.0850323i	0.255721	+	0.966751i	$0.417687\pi$
$390$		0			0
$391$	−5.17488	−	17.2853i	−0.261705	−	0.874155i
$392$	−9.55599	−	2.26481i	−0.482651	−	0.114390i
$393$		0			0
$394$	−2.29736	−	5.32587i	−0.115739	−	0.268313i
$395$	9.73351	+	8.16738i	0.489746	+	0.410946i
$396$		0			0
$397$	−0.858484	+	0.720353i	−0.0430861	+	0.0361535i	−0.664076	−	0.747665i	$-0.731175\pi$
$397$	−0.858484	+	0.720353i	−0.0430861	+	0.0361535i	0.620990	+	0.783818i	$0.286731\pi$
$398$	−1.86982	−	0.939061i	−0.0937258	−	0.0470709i
$399$		0			0
$400$	−19.9906	+	2.33656i	−0.999529	+	0.116828i
$401$	1.55567	−	26.7098i	0.0776863	−	1.33382i	−0.704022	−	0.710179i	$-0.748614\pi$
$401$	1.55567	−	26.7098i	0.0776863	−	1.33382i	0.781708	−	0.623645i	$-0.214349\pi$
$402$		0			0
$403$	−23.2935	−	24.6897i	−1.16033	−	1.22988i
$404$	0.163786			0.00814867
$405$		0			0
$406$	16.2901			0.808465
$407$	−1.66331	−	1.76300i	−0.0824471	−	0.0873889i
$408$		0			0
$409$	−0.296489	+	5.09052i	−0.0146604	+	0.251710i	0.983013	+	0.183536i	$0.0587543\pi$
$409$	−0.296489	+	5.09052i	−0.0146604	+	0.251710i	−0.997673	+	0.0681740i	$0.978283\pi$
$410$	4.28035	−	0.500301i	0.211391	−	0.0247081i
$411$		0			0
$412$	3.56073	+	1.78827i	0.175425	+	0.0881015i
$413$	−14.2882	+	11.9892i	−0.703075	+	0.589950i
$414$		0			0
$415$	−0.989713	−	0.830467i	−0.0485831	−	0.0407660i
$416$	4.02309	+	9.32657i	0.197248	+	0.457273i
$417$		0			0
$418$	1.97274	+	0.467548i	0.0964898	+	0.0228685i
$419$	−5.50879	−	18.4006i	−0.269122	−	0.898930i	−0.980566	−	0.196188i	$-0.937144\pi$
$419$	−5.50879	−	18.4006i	−0.269122	−	0.898930i	0.711444	−	0.702742i	$-0.248041\pi$
$420$		0			0
$421$	7.90539	+	0.924007i	0.385285	+	0.0450334i	0.306531	−	0.951861i	$-0.400832\pi$
$421$	7.90539	+	0.924007i	0.385285	+	0.0450334i	0.0787541	+	0.996894i	$0.474906\pi$
$422$	−1.28947	+	7.31297i	−0.0627706	+	0.355990i
$423$		0			0
$424$	0.348253	+	1.97504i	0.0169126	+	0.0959164i
$425$	−0.548712	−	9.42102i	−0.0266164	−	0.456986i
$426$		0			0
$427$	−11.0980	+	25.7280i	−0.537068	+	1.24506i
$428$	−6.75762	+	3.39380i	−0.326642	+	0.164046i
$429$		0			0
$430$	−3.08435	+	0.731004i	−0.148740	+	0.0352521i
$431$	−7.16012	−	12.4017i	−0.344891	−	0.597368i	0.640443	−	0.768005i	$-0.278751\pi$
$431$	−7.16012	−	12.4017i	−0.344891	−	0.597368i	−0.985334	+	0.170637i	$0.945417\pi$
$432$		0			0
$433$	−0.564188	+	0.977202i	−0.0271131	+	0.0469613i	−0.879264	−	0.476336i	$-0.841965\pi$
$433$	−0.564188	+	0.977202i	−0.0271131	+	0.0469613i	0.852150	+	0.523297i	$0.175298\pi$
$434$	13.1288	−	43.8533i	0.630204	−	2.10503i
$435$		0			0
$436$	−2.02856	−	1.33420i	−0.0971502	−	0.0638967i
$437$	−17.0164	−	22.8570i	−0.814005	−	1.09340i
$438$		0			0
$439$	9.26133	−	6.09127i	0.442019	−	0.290721i	−0.308925	−	0.951086i	$-0.599969\pi$
$439$	9.26133	−	6.09127i	0.442019	−	0.290721i	0.750944	+	0.660366i	$0.229599\pi$
$440$	0.714863	+	0.260189i	0.0340797	+	0.0124040i
$441$		0			0
$442$	−12.6941	+	4.62029i	−0.603798	+	0.219765i
$443$	−17.8223	+	23.9395i	−0.846763	+	1.13740i	0.142288	+	0.989825i	$0.454554\pi$
$443$	−17.8223	+	23.9395i	−0.846763	+	1.13740i	−0.989051	+	0.147574i	$0.952853\pi$
$444$		0			0
$445$	2.67468	−	2.83500i	0.126792	−	0.134392i
$446$	−3.24903	+	3.44377i	−0.153846	+	0.163067i
$447$		0			0
$448$	10.5942	−	14.2305i	0.500528	−	0.672326i
$449$	1.80790	−	0.658020i	0.0853199	−	0.0310539i	−0.299008	−	0.954251i	$-0.596656\pi$
$449$	1.80790	−	0.658020i	0.0853199	−	0.0310539i	0.384327	+	0.923197i	$0.374433\pi$
$450$		0			0
$451$	1.10701	+	0.402919i	0.0521271	+	0.0189727i
$452$	1.26093	−	0.829325i	0.0593091	−	0.0390082i
$453$		0			0
$454$	1.82979	+	2.45783i	0.0858763	+	0.115352i
$455$	9.26895	+	6.09628i	0.434535	+	0.285798i
$456$		0			0
$457$	−6.11136	+	20.4134i	−0.285877	+	0.954897i	0.687595	+	0.726094i	$0.258666\pi$
$457$	−6.11136	+	20.4134i	−0.285877	+	0.954897i	−0.973473	+	0.228803i	$0.926519\pi$
$458$	22.2797	−	38.5895i	1.04106	−	1.80317i
$459$		0			0
$460$	1.65018	+	2.85819i	0.0769399	+	0.133264i
$461$	−6.98761	+	1.65609i	−0.325446	+	0.0771320i	−0.390091	−	0.920776i	$-0.627556\pi$
$461$	−6.98761	+	1.65609i	−0.325446	+	0.0771320i	0.0646455	+	0.997908i	$0.479408\pi$
$462$		0			0
$463$	14.8572	−	7.46155i	0.690472	−	0.346768i	−0.0687192	−	0.997636i	$-0.521891\pi$
$463$	14.8572	−	7.46155i	0.690472	−	0.346768i	0.759191	+	0.650868i	$0.225595\pi$
$464$	−5.81862	+	13.4891i	−0.270123	+	0.626215i
$465$		0			0
$466$	0.145097	+	2.49122i	0.00672150	+	0.115404i
$467$	−4.26068	−	24.1635i	−0.197161	−	1.11815i	−0.909308	−	0.416124i	$-0.863388\pi$
$467$	−4.26068	−	24.1635i	−0.197161	−	1.11815i	0.712147	−	0.702031i	$-0.247723\pi$
$468$		0			0
$469$	−5.55860	+	31.5244i	−0.256672	+	1.45566i
$470$	17.4666	+	2.04155i	0.805672	+	0.0941696i
$471$		0			0
$472$	−3.86007	−	12.8935i	−0.177674	−	0.593473i
$473$	−0.843147	−	0.199830i	−0.0387679	−	0.00918817i
$474$		0			0
$475$	−5.90307	−	13.6848i	−0.270851	−	0.627904i
$476$	−2.66343	−	2.23488i	−0.122078	−	0.102436i
$477$		0			0
$478$	−26.5674	+	22.2927i	−1.21517	+	1.01965i
$479$	−18.6901	−	9.38653i	−0.853973	−	0.428881i	−0.0327330	−	0.999464i	$-0.510421\pi$
$479$	−18.6901	−	9.38653i	−0.853973	−	0.428881i	−0.821240	+	0.570583i	$0.806717\pi$
$480$		0			0
$481$	25.3333	−	2.96104i	1.15510	−	0.135012i
$482$	0.617294	−	10.5985i	0.0281170	−	0.482750i
$483$		0			0
$484$	3.51681	+	3.72760i	0.159855	+	0.169436i
$485$	4.06709			0.184677
$486$		0			0
$487$	19.1462			0.867597			0.433799	−	0.901010i	$-0.357173\pi$
$487$	19.1462			0.867597			0.433799	+	0.901010i	$0.357173\pi$
$488$	−13.8748	−	14.7064i	−0.628082	−	0.665728i
$489$		0			0
$490$	−0.320700	+	5.50620i	−0.0144877	+	0.248745i
$491$	7.08967	−	0.828664i	0.319952	−	0.0373971i	0.0453990	−	0.998969i	$-0.485544\pi$
$491$	7.08967	−	0.828664i	0.319952	−	0.0373971i	0.274553	+	0.961572i	$0.411470\pi$
$492$		0			0
$493$	−6.15542	−	3.09137i	−0.277226	−	0.139228i
$494$	−16.3430	+	13.7134i	−0.735309	+	0.616997i
$495$		0			0
$496$	31.6234	+	26.5352i	1.41993	+	1.19147i
$497$	19.0512	+	44.1656i	0.854562	+	1.98110i
$498$		0			0
$499$	19.8325	+	4.70039i	0.887825	+	0.210418i	0.649131	−	0.760676i	$-0.275133\pi$
$499$	19.8325	+	4.70039i	0.887825	+	0.210418i	0.238694	+	0.971095i	$0.423281\pi$
$500$	1.07568	+	3.59301i	0.0481057	+	0.160684i
$501$		0			0
$502$	16.0391	+	1.87470i	0.715859	+	0.0836719i
$503$	−2.25196	+	12.7715i	−0.100410	+	0.569453i	0.892545	+	0.450959i	$0.148918\pi$
$503$	−2.25196	+	12.7715i	−0.100410	+	0.569453i	−0.992955	+	0.118494i	$0.962193\pi$
$504$		0			0
$505$	0.0517499	+	0.293488i	0.00230284	+	0.0130601i
$506$	0.274869	+	4.71932i	0.0122194	+	0.209799i
$507$		0			0
$508$	0.864293	−	2.00366i	0.0383468	−	0.0888979i
$509$	−34.2187	+	17.1853i	−1.51672	+	0.761724i	−0.995771	−	0.0918658i	$-0.970717\pi$
$509$	−34.2187	+	17.1853i	−1.51672	+	0.761724i	−0.520946	+	0.853590i	$0.674421\pi$
$510$		0			0
$511$	22.1960	−	5.26054i	0.981891	−	0.232712i
$512$	5.16650	+	8.94865i	0.228329	+	0.395478i
$513$		0			0
$514$	19.0818	−	33.0507i	0.841664	−	1.45780i
$515$	−2.07934	+	6.94549i	−0.0916268	+	0.306055i
$516$		0			0
$517$	4.01637	+	2.64161i	0.176640	+	0.116178i
$518$	20.5405	+	27.5907i	0.902499	+	1.21227i
$519$		0			0
$520$	−6.68836	+	4.39900i	−0.293304	+	0.192909i
$521$	−30.1989	−	10.9915i	−1.32304	−	0.481546i	−0.418607	−	0.908167i	$-0.637482\pi$
$521$	−30.1989	−	10.9915i	−1.32304	−	0.481546i	−0.904431	+	0.426621i	$0.859704\pi$
$522$		0			0
$523$	−29.9071	+	10.8853i	−1.30775	+	0.475980i	−0.899512	−	0.436897i	$-0.856077\pi$
$523$	−29.9071	+	10.8853i	−1.30775	+	0.475980i	−0.408234	+	0.912877i	$0.633855\pi$
$524$	−0.706035	+	0.948370i	−0.0308433	+	0.0414297i
$525$		0			0
$526$	−15.6720	+	16.6113i	−0.683331	+	0.724288i
$527$	−13.2829	+	14.0791i	−0.578613	+	0.613294i
$528$		0			0
$529$	25.9430	−	34.8475i	1.12796	−	1.51511i
$530$	1.05841	−	0.385230i	0.0459745	−	0.0167333i
$531$		0			0
$532$	−5.15982	−	1.87802i	−0.223706	−	0.0814225i
$533$	−10.3573	+	6.81214i	−0.448627	+	0.295066i
$534$		0			0
$535$	−8.21649	−	11.0367i	−0.355230	−	0.477156i
$536$	−19.2985	−	12.6928i	−0.833569	−	0.548247i
$537$		0			0
$538$	5.30835	−	17.7311i	0.228859	−	0.764444i
$539$	−0.753872	+	1.30574i	−0.0324716	+	0.0562424i
$540$		0			0
$541$	−5.24207	−	9.07953i	−0.225374	−	0.390360i	0.731057	−	0.682316i	$-0.239027\pi$
$541$	−5.24207	−	9.07953i	−0.225374	−	0.390360i	−0.956432	+	0.291956i	$0.905694\pi$
$542$	−6.43070	+	1.52410i	−0.276222	+	0.0654659i
$543$		0			0
$544$	5.17600	−	2.59949i	0.221919	−	0.111452i
$545$	1.74981	−	4.05652i	0.0749538	−	0.173762i
$546$		0			0
$547$	1.46720	+	25.1908i	0.0627329	+	1.07708i	0.871957	+	0.489582i	$0.162851\pi$
$547$	1.46720	+	25.1908i	0.0627329	+	1.07708i	−0.809224	+	0.587500i	$0.800112\pi$
$548$	−0.785765	−	4.45630i	−0.0335662	−	0.190364i
$549$		0			0
$550$	−0.429341	+	2.43491i	−0.0183072	+	0.103825i
$551$	−10.8047	−	1.26289i	−0.460297	−	0.0538010i
$552$		0			0
$553$	−14.1373	−	47.2218i	−0.601178	−	2.00808i
$554$	−9.81456	−	2.32609i	−0.416981	−	0.0988263i
$555$		0			0
$556$	−3.73734	−	8.66412i	−0.158498	−	0.367441i
$557$	−24.7834	−	20.7958i	−1.05011	−	0.881145i	−0.0570029	−	0.998374i	$-0.518154\pi$
$557$	−24.7834	−	20.7958i	−1.05011	−	0.881145i	−0.993105	+	0.117229i	$0.962599\pi$
$558$		0			0
$559$	6.98501	−	5.86112i	0.295434	−	0.247899i
$560$	−12.0572	−	6.05536i	−0.509510	−	0.255885i
$561$		0			0
$562$	−3.17375	+	0.370958i	−0.133876	+	0.0156479i
$563$	−0.705719	+	12.1167i	−0.0297425	+	0.510659i	0.950233	+	0.311541i	$0.100845\pi$
$563$	−0.705719	+	12.1167i	−0.0297425	+	0.510659i	−0.979975	+	0.199119i	$0.936192\pi$
$564$		0			0
$565$	1.88447	+	1.99742i	0.0792803	+	0.0840322i
$566$	−11.7244			−0.492814
$567$		0			0
$568$	−34.7079			−1.45631
$569$	18.3928	+	19.4953i	0.771068	+	0.817284i	0.987268	−	0.159065i	$-0.0508479\pi$
$569$	18.3928	+	19.4953i	0.771068	+	0.817284i	−0.216200	+	0.976349i	$0.569366\pi$
$570$		0			0
$571$	1.30152	−	22.3462i	0.0544668	−	0.935159i	−0.854803	−	0.518952i	$-0.826322\pi$
$571$	1.30152	−	22.3462i	0.0544668	−	0.935159i	0.909270	−	0.416207i	$-0.136641\pi$
$572$	0.670896	−	0.0784165i	0.0280516	−	0.00327876i
$573$		0			0
$574$	−14.9400	−	7.50316i	−0.623585	−	0.313176i
$575$	26.6212	−	22.3378i	1.11018	−	0.931552i
$576$		0			0
$577$	−4.82667	−	4.05006i	−0.200937	−	0.168606i	0.536767	−	0.843731i	$-0.319645\pi$
$577$	−4.82667	−	4.05006i	−0.200937	−	0.168606i	−0.737704	+	0.675124i	$0.764090\pi$
$578$	−7.53487	−	17.4678i	−0.313409	−	0.726565i
$579$		0			0
$580$	1.22596	+	0.290558i	0.0509052	+	0.0120647i
$581$	1.43749	+	4.80156i	0.0596372	+	0.199202i
$582$		0			0
$583$	0.305818	+	0.0357449i	0.0126657	+	0.00148040i
$584$	−2.85825	+	16.2099i	−0.118275	+	0.670772i
$585$		0			0
$586$	5.98069	+	33.9182i	0.247060	+	1.40115i
$587$	−2.10905	−	36.2109i	−0.0870496	−	1.49458i	−0.705472	−	0.708738i	$-0.749265\pi$
$587$	−2.10905	−	36.2109i	−0.0870496	−	1.49458i	0.618422	−	0.785846i	$-0.287772\pi$
$588$		0			0
$589$	−12.1077	+	28.0688i	−0.498888	+	1.15655i
$590$	−6.75484	+	3.39241i	−0.278092	+	0.139663i
$591$		0			0
$592$	−30.1834	+	7.15360i	−1.24053	+	0.294011i
$593$	5.74524	+	9.95104i	0.235929	+	0.408640i	0.959542	−	0.281565i	$-0.0908535\pi$
$593$	5.74524	+	9.95104i	0.235929	+	0.408640i	−0.723614	+	0.690205i	$0.757520\pi$
$594$		0			0
$595$	3.16314	−	5.47872i	0.129676	−	0.224606i
$596$	−1.54781	+	5.17004i	−0.0634007	+	0.211773i
$597$		0			0
$598$	−41.5621	−	27.3358i	−1.69960	−	1.11784i
$599$	17.7397	+	23.8285i	0.724824	+	0.973607i	0.999926	+	0.0121920i	$0.00388092\pi$
$599$	17.7397	+	23.8285i	0.724824	+	0.973607i	−0.275102	+	0.961415i	$0.588712\pi$
$600$		0			0
$601$	−5.63532	+	3.70641i	−0.229869	+	0.151188i	−0.659219	−	0.751951i	$-0.729113\pi$
$601$	−5.63532	+	3.70641i	−0.229869	+	0.151188i	0.429350	+	0.903138i	$0.358743\pi$
$602$	11.5553	+	4.20580i	0.470960	+	0.171416i
$603$		0			0
$604$	−1.62621	+	0.591893i	−0.0661696	+	0.0240838i
$605$	−5.56831	+	7.47954i	−0.226384	+	0.304087i
$606$		0			0
$607$	0.115854	−	0.122798i	0.00470238	−	0.00498423i	−0.725018	−	0.688730i	$-0.758169\pi$
$607$	0.115854	−	0.122798i	0.00470238	−	0.00498423i	0.729721	+	0.683745i	$0.239650\pi$
$608$	6.27732	−	6.65358i	0.254579	−	0.269838i
$609$		0			0
$610$	−6.78084	+	9.10825i	−0.274548	+	0.368782i
$611$	−47.5360	+	17.3017i	−1.92310	+	0.699951i
$612$		0			0
$613$	−0.0309827	−	0.0112768i	−0.00125138	−	0.000455465i	0.341394	−	0.939920i	$-0.389101\pi$
$613$	−0.0309827	−	0.0112768i	−0.00125138	−	0.000455465i	−0.342646	+	0.939465i	$0.611323\pi$
$614$	−6.62601	+	4.35800i	−0.267404	+	0.175874i
$615$		0			0
$616$	−1.76235	−	2.36725i	−0.0710072	−	0.0953792i
$617$	33.1193	+	21.7829i	1.33333	+	0.876947i	0.997878	−	0.0651098i	$-0.0207398\pi$
$617$	33.1193	+	21.7829i	1.33333	+	0.876947i	0.335454	+	0.942056i	$0.391110\pi$
$618$		0			0
$619$	7.37777	−	24.6435i	0.296538	−	0.990505i	−0.671773	−	0.740757i	$-0.734467\pi$
$619$	7.37777	−	24.6435i	0.296538	−	0.990505i	0.968311	−	0.249748i	$-0.0803478\pi$
$620$	1.77023	−	3.06614i	0.0710943	−	0.123139i
$621$		0			0
$622$	−3.76169	−	6.51544i	−0.150830	−	0.261246i
$623$	−14.7128	+	3.48699i	−0.589455	+	0.139703i
$624$		0			0
$625$	12.9506	−	6.50406i	0.518026	−	0.260162i
$626$	8.99554	−	20.8540i	0.359534	−	0.833493i
$627$		0			0
$628$	−0.213747	−	3.66989i	−0.00852942	−	0.146445i
$629$	−2.52561	−	14.3235i	−0.100703	−	0.571114i
$630$		0			0
$631$	−1.47077	+	8.34112i	−0.0585502	+	0.332055i	−0.999987	−	0.00513523i	$-0.998365\pi$
$631$	−1.47077	+	8.34112i	−0.0585502	+	0.332055i	0.941437	+	0.337190i	$0.109477\pi$
$632$	35.3284	+	4.12930i	1.40529	+	0.164255i
$633$		0			0
$634$	−4.34391	−	14.5097i	−0.172519	−	0.576252i
$635$	3.86343	+	0.915651i	0.153316	+	0.0363365i
$636$		0			0
$637$	−6.28424	−	14.5685i	−0.248991	−	0.577225i
$638$	1.38246	+	1.16002i	0.0547320	+	0.0459256i
$639$		0			0
$640$	8.94859	−	7.50876i	0.353724	−	0.296810i
$641$	5.86128	+	2.94365i	0.231507	+	0.116267i	0.560772	−	0.827971i	$-0.310505\pi$
$641$	5.86128	+	2.94365i	0.231507	+	0.116267i	−0.329265	+	0.944238i	$0.606801\pi$
$642$		0			0
$643$	−30.8147	+	3.60172i	−1.21521	+	0.142038i	−0.699442	−	0.714690i	$-0.746568\pi$
$643$	−30.8147	+	3.60172i	−1.21521	+	0.142038i	−0.515770	+	0.856727i	$0.672494\pi$
$644$	0.744454	−	12.7818i	0.0293356	−	0.503673i
$645$		0			0
$646$	8.34862	+	8.84902i	0.328472	+	0.348160i
$647$	−2.59717			−0.102105			−0.0510526	−	0.998696i	$-0.516258\pi$
$647$	−2.59717			−0.102105			−0.0510526	+	0.998696i	$0.516258\pi$
$648$		0			0
$649$	−2.06631			−0.0811099
$650$	−17.8547	−	18.9248i	−0.700317	−	0.742293i
$651$		0			0
$652$	0.188276	−	3.23258i	0.00737347	−	0.126598i
$653$	36.3516	−	4.24890i	1.42255	−	0.166272i	0.630244	−	0.776397i	$-0.282955\pi$
$653$	36.3516	−	4.24890i	1.42255	−	0.166272i	0.792305	+	0.610125i	$0.208881\pi$
$654$		0			0
$655$	−1.92246	−	0.965497i	−0.0751168	−	0.0377251i
$656$	11.5494	−	9.69110i	0.450929	−	0.378374i
$657$		0			0
$658$	−52.2606	−	43.8518i	−2.03733	−	1.70952i
$659$	5.31974	+	12.3325i	0.207228	+	0.480408i	0.989855	−	0.142083i	$-0.0453800\pi$
$659$	5.31974	+	12.3325i	0.207228	+	0.480408i	−0.782627	+	0.622491i	$0.786121\pi$
$660$		0			0
$661$	24.3664	+	5.77494i	0.947742	+	0.224619i	0.675292	−	0.737551i	$-0.264018\pi$
$661$	24.3664	+	5.77494i	0.947742	+	0.224619i	0.272450	+	0.962170i	$0.412166\pi$
$662$	−4.78286	−	15.9759i	−0.185891	−	0.620919i
$663$		0			0
$664$	−3.59223	−	0.419871i	−0.139405	−	0.0162942i
$665$	1.73493	−	9.83925i	0.0672775	−	0.381550i
$666$		0			0
$667$	−4.40463	−	24.9799i	−0.170548	−	0.967224i
$668$	−0.492955	−	8.46371i	−0.0190730	−	0.327471i
$669$		0			0
$670$	−5.13820	+	11.9117i	−0.198506	+	0.460188i
$671$	−2.77391	+	1.39311i	−0.107086	+	0.0537805i
$672$		0			0
$673$	−7.49673	+	1.77676i	−0.288978	+	0.0684890i	−0.372548	−	0.928013i	$-0.621516\pi$
$673$	−7.49673	+	1.77676i	−0.288978	+	0.0684890i	0.0835703	+	0.996502i	$0.473368\pi$
$674$	−18.5151	−	32.0690i	−0.713173	−	1.23525i
$675$		0			0
$676$	−0.487788	+	0.844874i	−0.0187611	+	0.0324951i
$677$	−12.3771	+	41.3424i	−0.475691	+	1.58892i	0.297485	+	0.954727i	$0.403852\pi$
$677$	−12.3771	+	41.3424i	−0.475691	+	1.58892i	−0.773176	+	0.634192i	$0.781333\pi$
$678$		0			0
$679$	−13.1823	−	8.67011i	−0.505889	−	0.332728i
$680$	2.72601	+	3.66167i	0.104538	+	0.140418i
$681$		0			0
$682$	4.23697	−	2.78670i	0.162242	−	0.106708i
$683$	0.663970	+	0.241665i	0.0254061	+	0.00924707i	0.354692	−	0.934983i	$-0.384586\pi$
$683$	0.663970	+	0.241665i	0.0254061	+	0.00924707i	−0.329286	+	0.944230i	$0.606808\pi$
$684$		0			0
$685$	7.73697	−	2.81603i	0.295614	−	0.107595i
$686$	−9.10528	+	12.2305i	−0.347641	+	0.466963i
$687$		0			0
$688$	−7.61004	+	8.06618i	−0.290130	+	0.307520i
$689$	−2.22346	+	2.35672i	−0.0847069	+	0.0897841i
$690$		0			0
$691$	−17.4581	+	23.4502i	−0.664136	+	0.892089i	−0.998736	−	0.0502714i	$-0.983991\pi$
$691$	−17.4581	+	23.4502i	−0.664136	+	0.892089i	0.334600	+	0.942360i	$0.391399\pi$
$692$	5.03662	−	1.83318i	0.191463	−	0.0696870i
$693$		0			0
$694$	21.4627	+	7.81180i	0.814714	+	0.296532i
$695$	14.3444	−	9.43445i	0.544113	−	0.357869i
$696$		0			0
$697$	4.22140	+	5.67032i	0.159897	+	0.214779i
$698$	−35.0789	−	23.0718i	−1.32776	−	0.873280i
$699$		0			0
$700$	1.92056	−	6.41512i	0.0725904	−	0.242469i
$701$	15.3606	−	26.6053i	0.580160	−	1.00487i	−0.415299	−	0.909685i	$-0.636323\pi$
$701$	15.3606	−	26.6053i	0.580160	−	1.00487i	0.995460	−	0.0951826i	$-0.0303435\pi$
$702$		0			0
$703$	−11.4849	−	19.8925i	−0.433163	−	0.750259i
$704$	1.91242	−	0.453253i	0.0720772	−	0.0170826i
$705$		0			0
$706$	−15.7553	+	7.91261i	−0.592959	+	0.297795i
$707$	0.457919	−	1.06158i	0.0172218	−	0.0399247i
$708$		0			0
$709$	1.55476	+	26.6942i	0.0583902	+	1.00252i	0.892536	+	0.450976i	$0.148924\pi$
$709$	1.55476	+	26.6942i	0.0583902	+	1.00252i	−0.834146	+	0.551544i	$0.814039\pi$
$710$	3.38488	+	19.1966i	0.127032	+	0.720435i
$711$		0			0
$712$	1.89461	−	10.7449i	0.0710037	−	0.402682i
$713$	−70.7962	−	8.27489i	−2.65134	−	0.309897i
$714$		0			0
$715$	0.352491	+	1.17740i	0.0131824	+	0.0440323i
$716$	10.3125	+	2.44411i	0.385396	+	0.0913405i
$717$		0			0
$718$	−17.0491	−	39.5242i	−0.636266	−	1.47503i
$719$	32.8645	+	27.5766i	1.22564	+	1.02843i	0.998510	+	0.0545678i	$0.0173781\pi$
$719$	32.8645	+	27.5766i	1.22564	+	1.02843i	0.227128	+	0.973865i	$0.427066\pi$
$720$		0			0
$721$	21.5458	−	18.0791i	0.802407	−	0.673300i
$722$	−9.52439	−	4.78333i	−0.354461	−	0.178017i
$723$		0			0
$724$	−0.760226	+	0.0888576i	−0.0282536	+	0.00330237i
$725$	0.771378	−	13.2440i	0.0286482	−	0.491871i
$726$		0			0
$727$	−14.0051	−	14.8445i	−0.519419	−	0.550552i	0.413563	−	0.910475i	$-0.364284\pi$
$727$	−14.0051	−	14.8445i	−0.519419	−	0.550552i	−0.932982	+	0.359924i	$0.882803\pi$
$728$	31.0560			1.15101
$729$		0			0
$730$	9.24430			0.342147
$731$	−3.56819	−	3.78206i	−0.131974	−	0.139885i
$732$		0			0
$733$	−1.57474	+	27.0372i	−0.0581642	+	0.998641i	0.835382	+	0.549670i	$0.185247\pi$
$733$	−1.57474	+	27.0372i	−0.0581642	+	0.998641i	−0.893546	+	0.448971i	$0.851791\pi$
$734$	−4.95563	+	0.579230i	−0.182916	+	0.0213798i
$735$		0			0
$736$	19.0605	+	9.57255i	0.702580	+	0.352849i
$737$	−2.71658	+	2.27948i	−0.100066	+	0.0839657i
$738$		0			0
$739$	5.94808	+	4.99103i	0.218804	+	0.183598i	0.745601	−	0.666393i	$-0.232163\pi$
$739$	5.94808	+	4.99103i	0.218804	+	0.183598i	−0.526797	+	0.849991i	$0.676607\pi$
$740$	1.05372	+	2.44279i	0.0387354	+	0.0897987i
$741$		0			0
$742$	−4.25175	−	1.00768i	−0.156087	−	0.0369932i
$743$	2.95781	+	9.87977i	0.108511	+	0.362454i	0.994947	−	0.100398i	$-0.0320115\pi$
$743$	2.95781	+	9.87977i	0.108511	+	0.362454i	−0.886436	+	0.462851i	$0.846826\pi$
$744$		0			0
$745$	−9.75324	−	1.13999i	−0.357331	−	0.0417660i
$746$	6.55048	−	37.1496i	0.239830	−	1.36014i
$747$		0			0
$748$	−0.0668852	−	0.379325i	−0.00244557	−	0.0138695i
$749$	3.10366	+	53.2878i	0.113405	+	1.94709i
$750$		0			0
$751$	11.2748	−	26.1378i	0.411422	−	0.953783i	−0.578952	−	0.815362i	$-0.696538\pi$
$751$	11.2748	−	26.1378i	0.411422	−	0.953783i	0.990373	−	0.138421i	$-0.0442027\pi$
$752$	54.9785	−	27.6112i	2.00486	−	1.00688i
$753$		0			0
$754$	−18.4788	+	4.37955i	−0.672957	+	0.159494i
$755$	−1.57443	−	2.72699i	−0.0572994	−	0.0992455i
$756$		0			0
$757$	3.85089	−	6.66993i	0.139963	−	0.242423i	−0.787519	−	0.616290i	$-0.788635\pi$
$757$	3.85089	−	6.66993i	0.139963	−	0.242423i	0.927482	+	0.373867i	$0.121968\pi$
$758$	−4.31222	+	14.4038i	−0.156627	+	0.523170i
$759$		0			0
$760$	6.02337	+	3.96163i	0.218491	+	0.143704i
$761$	9.20606	+	12.3659i	0.333720	+	0.448263i	0.937033	−	0.349241i	$-0.113561\pi$
$761$	9.20606	+	12.3659i	0.333720	+	0.448263i	−0.603313	+	0.797504i	$0.706153\pi$
$762$		0			0
$763$	−14.3191	+	9.41782i	−0.518386	+	0.340948i
$764$	−1.62147	−	0.590166i	−0.0586626	−	0.0213514i
$765$		0			0
$766$	12.6856	−	4.61720i	0.458351	−	0.166826i
$767$	12.9846	−	17.4413i	0.468846	−	0.629770i
$768$		0			0
$769$	−25.1067	+	26.6115i	−0.905369	+	0.959635i	−0.999354	−	0.0359382i	$-0.988558\pi$
$769$	−25.1067	+	26.6115i	−0.905369	+	0.959635i	0.0939847	+	0.995574i	$0.470040\pi$
$770$	−1.13743	+	1.20561i	−0.0409901	+	0.0434470i
$771$		0			0
$772$	6.10046	−	8.19434i	0.219560	−	0.294921i
$773$	30.9114	−	11.2508i	1.11180	−	0.404664i	0.280149	−	0.959956i	$-0.409616\pi$
$773$	30.9114	−	11.2508i	1.11180	−	0.404664i	0.831655	+	0.555293i	$0.187394\pi$
$774$		0			0
$775$	−35.0316	−	12.7504i	−1.25837	−	0.458009i
$776$	9.51215	−	6.25624i	0.341466	−	0.224586i
$777$		0			0
$778$	−13.5626	−	18.2177i	−0.486242	−	0.653136i
$779$	9.32758	+	6.13484i	0.334195	+	0.219804i
$780$		0			0
$781$	−1.52826	+	5.10474i	−0.0546854	+	0.182662i

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)

\(f(q)\)	\(=\)	\(q+(-1.07889 - 1.14356i) q^{2} +(-0.0274281 + 0.470923i) q^{4} +(-0.852512 + 0.0996444i) q^{5} +(2.97559 + 1.49440i) q^{7} +(-1.84059 + 1.54444i) q^{8} +O(q^{10})\)	\(q+(-1.07889 - 1.14356i) q^{2} +(-0.0274281 + 0.470923i) q^{4} +(-0.852512 + 0.0996444i) q^{5} +(2.97559 + 1.49440i) q^{7} +(-1.84059 + 1.54444i) q^{8} +(1.03372 + 0.867390i) q^{10} +(0.146107 + 0.338713i) q^{11} +(-3.77713 - 0.895197i) q^{13} +(-1.50140 - 5.01504i) q^{14} +(4.68900 + 0.548065i) q^{16} +(-0.384378 + 2.17991i) q^{17} +(0.607044 + 3.44272i) q^{19} +(-0.0235420 - 0.404201i) q^{20} +(0.229704 - 0.532515i) q^{22} +(-7.28429 + 3.65831i) q^{23} +(-4.14838 + 0.983183i) q^{25} +(3.05140 + 5.28518i) q^{26} +(-0.785360 + 1.36028i) q^{28} +(-0.892472 + 2.98106i) q^{29} +(7.30581 + 4.80511i) q^{31} +(-1.56256 - 2.09889i) q^{32} +(2.90755 - 1.91233i) q^{34} +(-2.68563 - 0.977491i) q^{35} +(-6.17440 + 2.24730i) q^{37} +(3.28201 - 4.40850i) q^{38} +(1.41523 - 1.50006i) q^{40} +(2.19157 - 2.32293i) q^{41} +(-1.40273 + 1.88419i) q^{43} +(-0.163515 + 0.0595146i) q^{44} +(12.0424 + 4.38308i) q^{46} +(10.8880 - 7.16113i) q^{47} +(2.44079 + 3.27855i) q^{49} +(5.59996 + 3.68315i) q^{50} +(0.525168 - 1.75418i) q^{52} +(0.417342 - 0.722857i) q^{53} +(-0.158309 - 0.274198i) q^{55} +(-7.78483 + 1.84504i) q^{56} +(4.37189 - 2.19565i) q^{58} +(-2.21866 + 5.14344i) q^{59} +(0.489280 + 8.40062i) q^{61} +(-2.38725 - 13.5388i) q^{62} +(0.925198 - 5.24706i) q^{64} +(3.30926 + 0.386796i) q^{65} +(2.75718 + 9.20962i) q^{67} +(-1.01603 - 0.240803i) q^{68} +(1.77969 + 4.12577i) q^{70} +(11.0657 + 9.28524i) q^{71} +(5.24785 - 4.40347i) q^{73} +(9.23140 + 4.63618i) q^{74} +(-1.63790 + 0.191443i) q^{76} +(-0.0714187 + 1.22621i) q^{77} +(-10.1589 - 10.7678i) q^{79} -4.05204 q^{80} -5.02087 q^{82} +(1.03296 + 1.09488i) q^{83} +(0.110470 - 1.89670i) q^{85} +(3.66806 - 0.428735i) q^{86} +(-0.792043 - 0.397779i) q^{88} +(-3.47858 + 2.91888i) q^{89} +(-9.90141 - 8.30827i) q^{91} +(-1.52299 - 3.53068i) q^{92} +(-19.9361 - 4.72493i) q^{94} +(-0.860560 - 2.87447i) q^{95} +(-4.70641 - 0.550100i) q^{97} +(1.11586 - 6.32837i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more