LMFDB - Embedded newform 729.2.g.a.28.5

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			28.5
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.103498 - 0.0680719i) q^{2} +(-0.786081 + 1.82234i) q^{4} +(-2.31283 + 2.45146i) q^{5} +(3.71541 + 0.434269i) q^{7} +(0.0857144 + 0.486111i) q^{8} +O(q^{10})$	\(q+(0.103498 - 0.0680719i) q^{2} +(-0.786081 + 1.82234i) q^{4} +(-2.31283 + 2.45146i) q^{5} +(3.71541 + 0.434269i) q^{7} +(0.0857144 + 0.486111i) q^{8} +(-0.0724987 + 0.411161i) q^{10} +(-1.30961 + 4.37439i) q^{11} +(0.0739164 - 1.26910i) q^{13} +(0.414100 - 0.207969i) q^{14} +(-2.68194 - 2.84269i) q^{16} +(1.54764 - 0.563296i) q^{17} +(-4.14528 - 1.50876i) q^{19} +(-2.64932 - 6.14181i) q^{20} +(0.162231 + 0.541890i) q^{22} +(-1.06063 + 0.123970i) q^{23} +(-0.369733 - 6.34808i) q^{25} +(-0.0787396 - 0.136381i) q^{26} +(-3.71200 + 6.42938i) q^{28} +(-1.61142 - 0.809287i) q^{29} +(4.05312 + 5.44429i) q^{31} +(-1.43169 - 0.339317i) q^{32} +(0.121834 - 0.163651i) q^{34} +(-9.65772 + 8.10379i) q^{35} +(-2.46619 - 2.06938i) q^{37} +(-0.531734 + 0.126023i) q^{38} +(-1.38992 - 0.914167i) q^{40} +(-0.842295 - 0.553986i) q^{41} +(-2.24075 + 0.531068i) q^{43} +(-6.94218 - 5.82518i) q^{44} +(-0.101335 + 0.0850299i) q^{46} +(-5.68936 + 7.64213i) q^{47} +(6.80439 + 1.61267i) q^{49} +(-0.470392 - 0.631847i) q^{50} +(2.25462 + 1.13231i) q^{52} +(-1.43978 + 2.49378i) q^{53} +(-7.69474 - 13.3277i) q^{55} +(0.107361 + 1.84333i) q^{56} +(-0.221869 + 0.0259328i) q^{58} +(-3.05432 - 10.2021i) q^{59} +(2.10265 + 4.87448i) q^{61} +(0.790095 + 0.287571i) q^{62} +(7.17367 - 2.61100i) q^{64} +(2.94018 + 3.11641i) q^{65} +(-2.71756 + 1.36481i) q^{67} +(-0.190056 + 3.26313i) q^{68} +(-0.447917 + 1.49615i) q^{70} +(0.346694 - 1.96620i) q^{71} +(2.80114 + 15.8860i) q^{73} +(-0.396113 - 0.0462990i) q^{74} +(6.00801 - 6.36811i) q^{76} +(-6.76540 + 15.6840i) q^{77} +(4.69457 - 3.08767i) q^{79} +13.1716 q^{80} -0.124887 q^{82} +(10.0739 - 6.62572i) q^{83} +(-2.19854 + 5.09679i) q^{85} +(-0.195763 + 0.207497i) q^{86} +(-2.23869 - 0.261666i) q^{88} +(-1.69819 - 9.63089i) q^{89} +(0.825760 - 4.68312i) q^{91} +(0.607827 - 2.03028i) q^{92} +(-0.0686242 + 1.17823i) q^{94} +(13.2860 - 6.67248i) q^{95} +(6.44760 + 6.83405i) q^{97} +(0.814020 - 0.296279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.103498	−	0.0680719i	0.0731843	−	0.0481341i	−0.512390	−	0.858753i	$-0.671240\pi$
$2$	0.103498	−	0.0680719i	0.0731843	−	0.0481341i	0.585574	+	0.810619i	$0.300869\pi$
$3$		0			0
$3$		0			0
$4$	−0.786081	+	1.82234i	−0.393041	+	0.911171i
$5$	−2.31283	+	2.45146i	−1.03433	+	1.09633i	−0.0390538	+	0.999237i	$0.512434\pi$
$5$	−2.31283	+	2.45146i	−1.03433	+	1.09633i	−0.995276	+	0.0970882i	$0.969047\pi$
$6$		0			0
$7$	3.71541	+	0.434269i	1.40429	+	0.164138i	0.784258	−	0.620435i	$-0.213044\pi$
$7$	3.71541	+	0.434269i	1.40429	+	0.164138i	0.620036	+	0.784573i	$0.287118\pi$
$8$	0.0857144	+	0.486111i	0.0303046	+	0.171866i
$9$		0			0
$10$	−0.0724987	+	0.411161i	−0.0229261	+	0.130020i
$11$	−1.30961	+	4.37439i	−0.394861	+	1.31893i	0.497444	+	0.867496i	$0.334272\pi$
$11$	−1.30961	+	4.37439i	−0.394861	+	1.31893i	−0.892305	+	0.451433i	$0.850913\pi$
$12$		0			0
$13$	0.0739164	−	1.26910i	0.0205007	−	0.351984i	−0.972423	−	0.233226i	$-0.925072\pi$
$13$	0.0739164	−	1.26910i	0.0205007	−	0.351984i	0.992923	−	0.118758i	$-0.0378912\pi$
$14$	0.414100	−	0.207969i	0.110673	−	0.0555821i
$15$		0			0
$16$	−2.68194	−	2.84269i	−0.670486	−	0.710673i
$17$	1.54764	−	0.563296i	0.375359	−	0.136619i	−0.147450	−	0.989070i	$-0.547107\pi$
$17$	1.54764	−	0.563296i	0.375359	−	0.136619i	0.522808	+	0.852450i	$0.324884\pi$
$18$		0			0
$19$	−4.14528	−	1.50876i	−0.950993	−	0.346133i	−0.180495	−	0.983576i	$-0.557770\pi$
$19$	−4.14528	−	1.50876i	−0.950993	−	0.346133i	−0.770498	+	0.637443i	$0.779992\pi$
$20$	−2.64932	−	6.14181i	−0.592406	−	1.37335i
$21$		0			0
$22$	0.162231	+	0.541890i	0.0345878	+	0.115531i
$23$	−1.06063	+	0.123970i	−0.221157	+	0.0258495i	−0.225950	−	0.974139i	$-0.572548\pi$
$23$	−1.06063	+	0.123970i	−0.221157	+	0.0258495i	0.00479276	+	0.999989i	$0.498474\pi$
$24$		0			0
$25$	−0.369733	−	6.34808i	−0.0739467	−	1.26962i
$26$	−0.0787396	−	0.136381i	−0.0154421	−	0.0267465i
$27$		0			0
$28$	−3.71200	+	6.42938i	−0.701503	+	1.21504i
$29$	−1.61142	−	0.809287i	−0.299234	−	0.150281i	0.292847	−	0.956159i	$-0.405397\pi$
$29$	−1.61142	−	0.809287i	−0.299234	−	0.150281i	−0.592081	+	0.805878i	$0.701693\pi$
$30$		0			0
$31$	4.05312	+	5.44429i	0.727963	+	0.977823i	0.999880	+	0.0155028i	$0.00493490\pi$
$31$	4.05312	+	5.44429i	0.727963	+	0.977823i	−0.271917	+	0.962321i	$0.587658\pi$
$32$	−1.43169	−	0.339317i	−0.253090	−	0.0599834i
$33$		0			0
$34$	0.121834	−	0.163651i	0.0208943	−	0.0280659i
$35$	−9.65772	+	8.10379i	−1.63245	+	1.36979i
$36$		0			0
$37$	−2.46619	−	2.06938i	−0.405439	−	0.340204i	0.417152	−	0.908837i	$-0.363028\pi$
$37$	−2.46619	−	2.06938i	−0.405439	−	0.340204i	−0.822592	+	0.568633i	$0.807473\pi$
$38$	−0.531734	+	0.126023i	−0.0862586	+	0.0204437i
$39$		0			0
$40$	−1.38992	−	0.914167i	−0.219766	−	0.144542i
$41$	−0.842295	−	0.553986i	−0.131544	−	0.0865181i	0.482031	−	0.876154i	$-0.339899\pi$
$41$	−0.842295	−	0.553986i	−0.131544	−	0.0865181i	−0.613576	+	0.789636i	$0.710269\pi$
$42$		0			0
$43$	−2.24075	+	0.531068i	−0.341711	+	0.0809871i	−0.397889	−	0.917434i	$-0.630257\pi$
$43$	−2.24075	+	0.531068i	−0.341711	+	0.0809871i	0.0561773	+	0.998421i	$0.482109\pi$
$44$	−6.94218	−	5.82518i	−1.04657	−	0.878179i
$45$		0			0
$46$	−0.101335	+	0.0850299i	−0.0149410	+	0.0125370i
$47$	−5.68936	+	7.64213i	−0.829878	+	1.11472i	0.161908	+	0.986806i	$0.448235\pi$
$47$	−5.68936	+	7.64213i	−0.829878	+	1.11472i	−0.991785	+	0.127913i	$0.959172\pi$
$48$		0			0
$49$	6.80439	+	1.61267i	0.972055	+	0.230381i
$50$	−0.470392	−	0.631847i	−0.0665235	−	0.0893566i
$51$		0			0
$52$	2.25462	+	1.13231i	0.312660	+	0.157024i
$53$	−1.43978	+	2.49378i	−0.197769	+	0.342547i	−0.947805	−	0.318851i	$-0.896703\pi$
$53$	−1.43978	+	2.49378i	−0.197769	+	0.342547i	0.750035	+	0.661398i	$0.230036\pi$
$54$		0			0
$55$	−7.69474	−	13.3277i	−1.03756	−	1.79710i
$56$	0.107361	+	1.84333i	0.0143468	+	0.246325i
$57$		0			0
$58$	−0.221869	+	0.0259328i	−0.0291328	+	0.00340514i
$59$	−3.05432	−	10.2021i	−0.397638	−	1.32820i	−0.889263	−	0.457397i	$-0.848782\pi$
$59$	−3.05432	−	10.2021i	−0.397638	−	1.32820i	0.491625	−	0.870807i	$-0.336403\pi$
$60$		0			0
$61$	2.10265	+	4.87448i	0.269216	+	0.624114i	0.998171	−	0.0604479i	$-0.0192529\pi$
$61$	2.10265	+	4.87448i	0.269216	+	0.624114i	−0.728955	+	0.684562i	$0.759994\pi$
$62$	0.790095	+	0.287571i	0.100342	+	0.0365215i
$63$		0			0
$64$	7.17367	−	2.61100i	0.896708	−	0.326375i
$65$	2.94018	+	3.11641i	0.364684	+	0.386543i
$66$		0			0
$67$	−2.71756	+	1.36481i	−0.332002	+	0.166738i	−0.606989	−	0.794710i	$-0.707623\pi$
$67$	−2.71756	+	1.36481i	−0.332002	+	0.166738i	0.274987	+	0.961448i	$0.411327\pi$
$68$	−0.190056	+	3.26313i	−0.0230476	+	0.395713i
$69$		0			0
$70$	−0.447917	+	1.49615i	−0.0535363	+	0.178824i
$71$	0.346694	−	1.96620i	0.0411451	−	0.233345i	−0.957300	−	0.289098i	$-0.906645\pi$
$71$	0.346694	−	1.96620i	0.0411451	−	0.233345i	0.998445	+	0.0557526i	$0.0177558\pi$
$72$		0			0
$73$	2.80114	+	15.8860i	0.327848	+	1.85932i	0.488854	+	0.872366i	$0.337415\pi$
$73$	2.80114	+	15.8860i	0.327848	+	1.85932i	−0.161006	+	0.986953i	$0.551474\pi$
$74$	−0.396113	−	0.0462990i	−0.0460472	−	0.00538215i
$75$		0			0
$76$	6.00801	−	6.36811i	0.689166	−	0.730473i
$77$	−6.76540	+	15.6840i	−0.770989	+	1.78735i
$78$		0			0
$79$	4.69457	−	3.08767i	0.528181	−	0.347390i	−0.257245	−	0.966346i	$-0.582815\pi$
$79$	4.69457	−	3.08767i	0.528181	−	0.347390i	0.785425	+	0.618956i	$0.212444\pi$
$80$	13.1716			1.47263
$81$		0			0
$82$	−0.124887			−0.0137915
$83$	10.0739	−	6.62572i	1.10576	−	0.727267i	0.140894	−	0.990025i	$-0.455002\pi$
$83$	10.0739	−	6.62572i	1.10576	−	0.727267i	0.964862	+	0.262758i	$0.0846320\pi$
$84$		0			0
$85$	−2.19854	+	5.09679i	−0.238465	+	0.552825i
$86$	−0.195763	+	0.207497i	−0.0211097	+	0.0223750i
$87$		0			0
$88$	−2.23869	−	0.261666i	−0.238645	−	0.0278936i
$89$	−1.69819	−	9.63089i	−0.180007	−	1.02087i	−0.932204	−	0.361934i	$-0.882117\pi$
$89$	−1.69819	−	9.63089i	−0.180007	−	1.02087i	0.752197	−	0.658939i	$-0.228994\pi$
$90$		0			0
$91$	0.825760	−	4.68312i	0.0865631	−	0.490924i
$92$	0.607827	−	2.03028i	0.0633703	−	0.211672i
$93$		0			0
$94$	−0.0686242	+	1.17823i	−0.00707805	+	0.121525i
$95$	13.2860	−	6.67248i	1.36312	−	0.684582i
$96$		0			0
$97$	6.44760	+	6.83405i	0.654654	+	0.693893i	0.966624	−	0.256199i	$-0.0824702\pi$
$97$	6.44760	+	6.83405i	0.654654	+	0.693893i	−0.311970	+	0.950092i	$0.600989\pi$
$98$	0.814020	−	0.296279i	0.0822284	−	0.0299287i
$99$		0			0
$100$	11.8590	+	4.31632i	1.18590	+	0.431632i
$101$	2.16870	+	5.02761i	0.215794	+	0.500266i	0.991387	−	0.130967i	$-0.0418083\pi$
$101$	2.16870	+	5.02761i	0.215794	+	0.500266i	−0.775593	+	0.631233i	$0.782549\pi$
$102$		0			0
$103$	0.672471	+	2.24621i	0.0662606	+	0.221326i	0.984707	−	0.174220i	$-0.0557405\pi$
$103$	0.672471	+	2.24621i	0.0662606	+	0.221326i	−0.918446	+	0.395546i	$0.870555\pi$
$104$	0.623257	−	0.0728483i	0.0611154	−	0.00714336i
$105$		0			0
$106$	0.0207411	+	0.356111i	0.00201455	+	0.0345885i
$107$	5.88377	+	10.1910i	0.568805	+	0.985200i	0.996684	+	0.0813640i	$0.0259276\pi$
$107$	5.88377	+	10.1910i	0.568805	+	0.985200i	−0.427879	+	0.903836i	$0.640739\pi$
$108$		0			0
$109$	−0.211790	+	0.366831i	−0.0202858	+	0.0351361i	−0.875990	−	0.482329i	$-0.839791\pi$
$109$	−0.211790	+	0.366831i	−0.0202858	+	0.0351361i	0.855704	+	0.517465i	$0.173124\pi$
$110$	−1.70363	−	0.855597i	−0.162435	−	0.0815779i
$111$		0			0
$112$	−8.73003	−	11.7265i	−0.824910	−	1.10805i
$113$	13.3588	+	3.16609i	1.25669	+	0.297840i	0.804430	−	0.594047i	$-0.202471\pi$
$113$	13.3588	+	3.16609i	1.25669	+	0.297840i	0.452257	+	0.891888i	$0.350619\pi$
$114$		0			0
$115$	2.14915	−	2.88681i	0.200410	−	0.269197i
$116$	2.74151	−	2.30040i	0.254542	−	0.213586i
$117$		0			0
$118$	−1.01059	−	0.847990i	−0.0930328	−	0.0780638i
$119$	5.99475	−	1.42078i	0.549538	−	0.130243i
$120$		0			0
$121$	−8.22988	−	5.41288i	−0.748171	−	0.492080i
$122$	0.549436	+	0.361370i	0.0497436	+	0.0327169i
$123$		0			0
$124$	−13.1074	+	3.10652i	−1.17708	+	0.278974i
$125$	3.50823	+	2.94375i	0.313785	+	0.263297i
$126$		0			0
$127$	2.77429	−	2.32790i	0.246178	−	0.206568i	−0.511346	−	0.859375i	$-0.670853\pi$
$127$	2.77429	−	2.32790i	0.246178	−	0.206568i	0.757524	+	0.652807i	$0.226409\pi$
$128$	2.32199	−	3.11897i	0.205237	−	0.275681i
$129$		0			0
$130$	0.516443	+	0.122399i	0.0452951	+	0.0107351i
$131$	3.73212	+	5.01310i	0.326077	+	0.437997i	0.934687	−	0.355473i	$-0.115680\pi$
$131$	3.73212	+	5.01310i	0.326077	+	0.437997i	−0.608610	+	0.793469i	$0.708273\pi$
$132$		0			0
$133$	−14.7462	−	7.40584i	−1.27866	−	0.642167i
$134$	−0.188357	+	0.326245i	−0.0162716	+	0.0281832i
$135$		0			0
$136$	0.406480	+	0.704043i	0.0348553	+	0.0603712i
$137$	−0.952195	−	16.3486i	−0.0813515	−	1.39675i	−0.754041	−	0.656827i	$-0.771898\pi$
$137$	−0.952195	−	16.3486i	−0.0813515	−	1.39675i	0.672690	−	0.739925i	$-0.265139\pi$
$138$		0			0
$139$	−19.4102	+	2.26873i	−1.64635	+	0.192431i	−0.888139	−	0.459574i	$-0.848002\pi$
$139$	−19.4102	+	2.26873i	−1.64635	+	0.192431i	−0.758214	+	0.652006i	$0.773928\pi$
$140$	−7.17612	−	23.9699i	−0.606492	−	2.02583i
$141$		0			0
$142$	−0.0979608	−	0.227099i	−0.00822069	−	0.0190577i
$143$	5.45472	+	1.98536i	0.456147	+	0.166024i
$144$		0			0
$145$	5.71088	−	2.07859i	0.474263	−	0.172617i
$146$	1.37131	+	1.45350i	0.113490	+	0.120292i
$147$		0			0
$148$	5.70974	−	2.86754i	0.469338	−	0.235710i
$149$	−0.238124	+	4.08844i	−0.0195079	+	0.334938i	0.974407	+	0.224790i	$0.0721695\pi$
$149$	−0.238124	+	4.08844i	−0.0195079	+	0.334938i	−0.993915	+	0.110148i	$0.964868\pi$
$150$		0			0
$151$	−2.54334	+	8.49534i	−0.206974	+	0.691341i	0.789965	+	0.613152i	$0.210099\pi$
$151$	−2.54334	+	8.49534i	−0.206974	+	0.691341i	−0.996939	+	0.0781885i	$0.975086\pi$
$152$	0.378114	−	2.14439i	0.0306691	−	0.173933i
$153$		0			0
$154$	0.367429	+	2.08380i	0.0296083	+	0.167917i
$155$	−22.7206	−	2.65566i	−1.82497	−	0.213308i
$156$		0			0
$157$	−3.63877	+	3.85687i	−0.290406	+	0.307812i	−0.856107	−	0.516798i	$-0.827124\pi$
$157$	−3.63877	+	3.85687i	−0.290406	+	0.307812i	0.565702	+	0.824610i	$0.308605\pi$
$158$	0.275697	−	0.639137i	0.0219333	−	0.0508470i
$159$		0			0
$160$	4.14309	−	2.72495i	0.327540	−	0.215426i
$161$	−3.99452			−0.314812
$162$		0			0
$163$	−4.86655			−0.381178			−0.190589	−	0.981670i	$-0.561040\pi$
$163$	−4.86655			−0.381178			−0.190589	+	0.981670i	$0.561040\pi$
$164$	1.67166	−	1.09947i	0.130535	−	0.0858543i
$165$		0			0
$166$	0.591608	−	1.37150i	0.0459177	−	0.106449i
$167$	−15.3368	+	16.2561i	−1.18680	+	1.25793i	−0.228060	+	0.973647i	$0.573238\pi$
$167$	−15.3368	+	16.2561i	−1.18680	+	1.25793i	−0.958739	+	0.284286i	$0.908243\pi$
$168$		0			0
$169$	11.3070	+	1.32159i	0.869766	+	0.101661i
$170$	0.119403	+	0.677168i	0.00915779	+	0.0519364i
$171$		0			0
$172$	0.793626	−	4.50088i	0.0605134	−	0.343189i
$173$	−1.00106	+	3.34376i	−0.0761089	+	0.254221i	−0.987574	−	0.157157i	$-0.949767\pi$
$173$	−1.00106	+	3.34376i	−0.0761089	+	0.254221i	0.911465	+	0.411378i	$0.134952\pi$
$174$		0			0
$175$	1.38306	−	23.7463i	0.104550	−	1.79505i
$176$	15.9474	−	8.00906i	1.20208	−	0.603706i
$177$		0			0
$178$	−0.831352	−	0.881182i	−0.0623125	−	0.0660474i
$179$	14.1428	−	5.14757i	1.05709	−	0.384748i	0.245753	−	0.969333i	$-0.420965\pi$
$179$	14.1428	−	5.14757i	1.05709	−	0.384748i	0.811332	+	0.584585i	$0.198743\pi$
$180$		0			0
$181$	−2.01428	−	0.733137i	−0.149720	−	0.0544936i	0.266073	−	0.963953i	$-0.414274\pi$
$181$	−2.01428	−	0.733137i	−0.149720	−	0.0544936i	−0.415793	+	0.909459i	$0.636496\pi$
$182$	−0.233324	−	0.540906i	−0.0172951	−	0.0400946i
$183$		0			0
$184$	−0.151175	−	0.504958i	−0.0111447	−	0.0372260i
$185$	10.7769	−	1.25964i	0.792332	−	0.0926103i
$186$		0			0
$187$	0.437273	+	7.50769i	0.0319766	+	0.549017i
$188$	−9.45428	−	16.3753i	−0.689524	−	1.19429i
$189$		0			0
$190$	0.920870	−	1.59499i	0.0668069	−	0.115713i
$191$	18.6097	+	9.34613i	1.34655	+	0.676262i	0.968381	−	0.249475i	$-0.0802580\pi$
$191$	18.6097	+	9.34613i	1.34655	+	0.676262i	0.378168	+	0.925737i	$0.376554\pi$
$192$		0			0
$193$	8.41707	+	11.3061i	0.605874	+	0.813830i	0.994184	−	0.107699i	$-0.0343484\pi$
$193$	8.41707	+	11.3061i	0.605874	+	0.813830i	−0.388310	+	0.921529i	$0.626941\pi$
$194$	1.13252	+	0.268413i	0.0813104	+	0.0192709i
$195$		0			0
$196$	−8.28764	+	11.1322i	−0.591974	+	0.795159i
$197$	−1.46772	+	1.23157i	−0.104571	+	0.0877455i	−0.693574	−	0.720385i	$-0.743965\pi$
$197$	−1.46772	+	1.23157i	−0.104571	+	0.0877455i	0.589003	+	0.808131i	$0.299521\pi$
$198$		0			0
$199$	12.3341	+	10.3495i	0.874339	+	0.733658i	0.965007	−	0.262223i	$-0.0844557\pi$
$199$	12.3341	+	10.3495i	0.874339	+	0.733658i	−0.0906679	+	0.995881i	$0.528900\pi$
$200$	3.05418	−	0.723853i	0.215963	−	0.0511841i
$201$		0			0
$202$	0.566696	+	0.372722i	0.0398726	+	0.0262246i
$203$	−5.63565	−	3.70662i	−0.395545	−	0.260154i
$204$		0			0
$205$	3.30616	−	0.783574i	0.230912	−	0.0547272i
$206$	0.222503	+	0.186703i	0.0155025	+	0.0130082i
$207$		0			0
$208$	−3.80589	+	3.19352i	−0.263891	+	0.221431i
$209$	12.0286	−	16.1572i	0.832036	−	1.11762i
$210$		0			0
$211$	3.75461	+	0.889860i	0.258478	+	0.0612605i	0.357812	−	0.933794i	$-0.383523\pi$
$211$	3.75461	+	0.889860i	0.258478	+	0.0612605i	−0.0993336	+	0.995054i	$0.531671\pi$
$212$	−3.41273	−	4.58409i	−0.234387	−	0.314837i
$213$		0			0
$214$	1.30268	+	0.654231i	0.0890494	+	0.0447223i
$215$	3.88059	−	6.72138i	0.264654	−	0.458394i
$216$		0			0
$217$	12.6947	+	21.9879i	0.861775	+	1.49264i
$218$	0.00305098	+	0.0523834i	0.000206639	+	0.00354785i
$219$		0			0
$220$	30.3363	−	3.54580i	2.04527	−	0.239058i
$221$	−0.600480	−	2.00574i	−0.0403927	−	0.134921i
$222$		0			0
$223$	1.18505	+	2.74725i	0.0793567	+	0.183970i	0.953275	−	0.302103i	$-0.0976885\pi$
$223$	1.18505	+	2.74725i	0.0793567	+	0.183970i	−0.873919	+	0.486072i	$0.838429\pi$
$224$	−5.17198	−	1.88245i	−0.345567	−	0.125776i
$225$		0			0
$226$	1.59813	−	0.581672i	0.106306	−	0.0386923i
$227$	16.4925	+	17.4810i	1.09465	+	1.16026i	0.986098	+	0.166167i	$0.0531390\pi$
$227$	16.4925	+	17.4810i	1.09465	+	1.16026i	0.108549	+	0.994091i	$0.465380\pi$
$228$		0			0
$229$	−4.22971	+	2.12424i	−0.279507	+	0.140374i	−0.583031	−	0.812450i	$-0.698133\pi$
$229$	−4.22971	+	2.12424i	−0.279507	+	0.140374i	0.303523	+	0.952824i	$0.401837\pi$
$230$	0.0259228	−	0.445077i	0.00170930	−	0.0293475i
$231$		0			0
$232$	0.255281	−	0.852697i	0.0167600	−	0.0559823i
$233$	1.81475	−	10.2920i	0.118888	−	0.674250i	−0.865863	−	0.500282i	$-0.833230\pi$
$233$	1.81475	−	10.2920i	0.118888	−	0.674250i	0.984751	−	0.173968i	$-0.0556591\pi$
$234$		0			0
$235$	−5.57584	−	31.6222i	−0.363728	−	2.06280i
$236$	20.9927	+	2.45370i	1.36651	+	0.159722i
$237$		0			0
$238$	0.523731	−	0.555123i	0.0339485	−	0.0359833i
$239$	6.26895	−	14.5331i	0.405504	−	0.940065i	−0.586038	−	0.810283i	$-0.699313\pi$
$239$	6.26895	−	14.5331i	0.405504	−	0.940065i	0.991543	−	0.129782i	$-0.0414276\pi$
$240$		0			0
$241$	−14.7387	+	9.69379i	−0.949402	+	0.624432i	−0.926897	−	0.375315i	$-0.877535\pi$
$241$	−14.7387	+	9.69379i	−0.949402	+	0.624432i	−0.0225049	+	0.999747i	$0.507164\pi$
$242$	−1.22024			−0.0784402
$243$		0			0
$244$	−10.5358			−0.674487
$245$	−19.6908	+	12.9508i	−1.25800	+	0.827399i
$246$		0			0
$247$	−2.22117	+	5.14924i	−0.141329	+	0.327638i
$248$	−2.29912	+	2.43692i	−0.145994	+	0.154745i
$249$		0			0
$250$	0.563482	+	0.0658616i	0.0356377	+	0.00416545i
$251$	3.58499	+	20.3315i	0.226282	+	1.28331i	0.860218	+	0.509926i	$0.170327\pi$
$251$	3.58499	+	20.3315i	0.226282	+	1.28331i	−0.633936	+	0.773386i	$0.718562\pi$
$252$		0			0
$253$	0.846717	−	4.80197i	0.0532326	−	0.301897i
$254$	0.128669	−	0.429785i	0.00807342	−	0.0269671i
$255$		0			0
$256$	−0.859754	+	14.7614i	−0.0537346	+	0.922588i
$257$	−6.51246	+	3.27068i	−0.406236	+	0.204019i	−0.640170	−	0.768233i	$-0.721136\pi$
$257$	−6.51246	+	3.27068i	−0.406236	+	0.204019i	0.233934	+	0.972252i	$0.424840\pi$
$258$		0			0
$259$	−8.26425	−	8.75959i	−0.513515	−	0.544294i
$260$	−7.99038	+	2.90826i	−0.495542	+	0.180363i
$261$		0			0
$262$	0.727519	+	0.264795i	0.0449463	+	0.0163591i
$263$	4.13582	+	9.58791i	0.255026	+	0.591216i	0.996844	−	0.0793849i	$-0.0252956\pi$
$263$	4.13582	+	9.58791i	0.255026	+	0.591216i	−0.741818	+	0.670601i	$0.766036\pi$
$264$		0			0
$265$	−2.78342	−	9.29726i	−0.170984	−	0.571126i
$266$	−2.03034	+	0.237313i	−0.124488	+	0.0145506i
$267$		0			0
$268$	−0.350926	−	6.02517i	−0.0214362	−	0.368046i
$269$	11.1578	+	19.3259i	0.680304	+	1.17832i	0.974888	+	0.222695i	$0.0714854\pi$
$269$	11.1578	+	19.3259i	0.680304	+	1.17832i	−0.294585	+	0.955625i	$0.595181\pi$
$270$		0			0
$271$	11.6312	−	20.1458i	0.706544	−	1.22377i	−0.259588	−	0.965720i	$-0.583587\pi$
$271$	11.6312	−	20.1458i	0.706544	−	1.22377i	0.966132	−	0.258050i	$-0.0830800\pi$
$272$	−5.75197	−	2.88875i	−0.348764	−	0.175156i
$273$		0			0
$274$	−1.21143	−	1.62723i	−0.0731850	−	0.0983046i
$275$	28.2532	+	6.69613i	1.70373	+	0.403792i
$276$		0			0
$277$	5.29170	−	7.10799i	0.317948	−	0.427078i	−0.614203	−	0.789148i	$-0.710522\pi$
$277$	5.29170	−	7.10799i	0.317948	−	0.427078i	0.932151	+	0.362070i	$0.117930\pi$
$278$	−1.85449	+	1.55610i	−0.111225	+	0.0933287i
$279$		0			0
$280$	−4.76714	−	4.00011i	−0.284891	−	0.239052i
$281$	−20.9045	+	4.95445i	−1.24706	+	0.295558i	−0.800574	−	0.599234i	$-0.795472\pi$
$281$	−20.9045	+	4.95445i	−1.24706	+	0.295558i	−0.446483	+	0.894792i	$0.647324\pi$
$282$		0			0
$283$	0.511009	+	0.336096i	0.0303763	+	0.0199788i	0.564606	−	0.825360i	$-0.309028\pi$
$283$	0.511009	+	0.336096i	0.0303763	+	0.0199788i	−0.534230	+	0.845339i	$0.679398\pi$
$284$	3.31056	+	2.17739i	0.196446	+	0.129204i
$285$		0			0
$286$	0.699702	−	0.165832i	0.0413742	−	0.00980587i
$287$	−2.88890	−	2.42407i	−0.170526	−	0.143088i
$288$		0			0
$289$	−10.9449	+	9.18383i	−0.643815	+	0.540225i
$290$	0.449573	−	0.603881i	0.0263998	−	0.0354611i
$291$		0			0
$292$	−31.1517	−	7.38309i	−1.82302	−	0.432063i
$293$	−18.4868	−	24.8321i	−1.08001	−	1.45071i	−0.882443	−	0.470419i	$-0.844103\pi$
$293$	−18.4868	−	24.8321i	−1.08001	−	1.45071i	−0.197569	−	0.980289i	$-0.563305\pi$
$294$		0			0
$295$	32.0742	+	16.1083i	1.86743	+	0.937860i
$296$	0.794559	−	1.37622i	0.0461828	−	0.0799910i
$297$		0			0
$298$	0.253662	+	0.439356i	0.0146943	+	0.0254512i
$299$	0.0789318	+	1.35521i	0.00456474	+	0.0783736i
$300$		0			0
$301$	−8.55594	+	1.00005i	−0.493156	+	0.0576417i
$302$	0.315063	+	1.05238i	0.0181298	+	0.0605578i
$303$		0			0
$304$	6.82847	+	15.8302i	0.391640	+	0.907923i
$305$	−16.8127	−	6.11931i	−0.962690	−	0.350391i
$306$		0			0
$307$	−21.3773	+	7.78069i	−1.22007	+	0.444068i	−0.870184	−	0.492726i	$-0.836000\pi$
$307$	−21.3773	+	7.78069i	−1.22007	+	0.444068i	−0.349882	+	0.936794i	$0.613778\pi$
$308$	−23.2634	−	24.6577i	−1.32555	−	1.40500i
$309$		0			0
$310$	−2.53232	+	1.27178i	−0.143826	+	0.0722323i
$311$	−1.78117	+	30.5816i	−0.101001	+	1.73412i	0.444298	+	0.895879i	$0.353453\pi$
$311$	−1.78117	+	30.5816i	−0.101001	+	1.73412i	−0.545299	+	0.838242i	$0.683584\pi$
$312$		0			0
$313$	6.54199	−	21.8518i	0.369775	−	1.23513i	−0.547475	−	0.836822i	$-0.684411\pi$
$313$	6.54199	−	21.8518i	0.369775	−	1.23513i	0.917250	−	0.398312i	$-0.130404\pi$
$314$	−0.114062	+	0.646878i	−0.00643689	+	0.0365054i
$315$		0			0
$316$	1.93647	+	10.9823i	0.108935	+	0.617801i
$317$	−7.96795	−	0.931320i	−0.447525	−	0.0523081i	−0.110654	−	0.993859i	$-0.535294\pi$
$317$	−7.96795	−	0.931320i	−0.447525	−	0.0523081i	−0.336871	+	0.941551i	$0.609369\pi$
$318$		0			0
$319$	5.65047	−	5.98915i	0.316365	−	0.335328i
$320$	−10.1907	+	23.6247i	−0.569679	+	1.32066i
$321$		0			0
$322$	−0.413426	+	0.271915i	−0.0230393	+	0.0151532i
$323$	−7.26530			−0.404252
$324$		0			0
$325$	−8.08365			−0.448400
$326$	−0.503680	+	0.331275i	−0.0278962	+	0.0183476i
$327$		0			0
$328$	0.197102	−	0.456933i	0.0108831	−	0.0252299i
$329$	−24.4570	+	25.9230i	−1.34836	+	1.42918i
$330$		0			0
$331$	−18.2750	−	2.13604i	−1.00448	−	0.117407i	−0.402085	−	0.915602i	$-0.631714\pi$
$331$	−18.2750	−	2.13604i	−1.00448	−	0.117407i	−0.602399	+	0.798195i	$0.705788\pi$
$332$	4.15540	+	23.5665i	0.228057	+	1.29338i
$333$		0			0
$334$	−0.480753	+	2.72648i	−0.0263056	+	0.149187i
$335$	2.93948	−	9.81855i	0.160601	−	0.536445i
$336$		0			0
$337$	−1.55141	+	26.6366i	−0.0845105	+	1.45099i	0.643512	+	0.765436i	$0.277477\pi$
$337$	−1.55141	+	26.6366i	−0.0845105	+	1.45099i	−0.728022	+	0.685553i	$0.759560\pi$
$338$	1.26021	−	0.632903i	0.0685466	−	0.0344254i
$339$		0			0
$340$	−7.55986	−	8.01298i	−0.409991	−	0.434565i
$341$	−29.1235	+	10.6001i	−1.57712	+	0.574026i
$342$		0			0
$343$	−0.0250188	−	0.00910611i	−0.00135089	−	0.000491683i
$344$	−0.450222	−	1.04373i	−0.0242744	−	0.0562743i
$345$		0			0
$346$	0.124009	+	0.414217i	0.00666674	+	0.0222685i
$347$	24.3715	−	2.84862i	1.30833	−	0.152922i	0.566807	−	0.823850i	$-0.308178\pi$
$347$	24.3715	−	2.84862i	1.30833	−	0.152922i	0.741522	+	0.670929i	$0.234104\pi$
$348$		0			0
$349$	−0.975561	−	16.7497i	−0.0522206	−	0.896592i	−0.918102	−	0.396344i	$-0.870279\pi$
$349$	−0.975561	−	16.7497i	−0.0522206	−	0.896592i	0.865882	−	0.500249i	$-0.166758\pi$
$350$	−1.47331	−	2.55185i	−0.0787517	−	0.136402i
$351$		0			0
$352$	3.35926	−	5.81841i	0.179049	−	0.310123i
$353$	−17.5821	−	8.83007i	−0.935802	−	0.469977i	−0.0855386	−	0.996335i	$-0.527261\pi$
$353$	−17.5821	−	8.83007i	−0.935802	−	0.469977i	−0.850263	+	0.526357i	$0.823557\pi$
$354$		0			0
$355$	4.01822	+	5.39740i	0.213265	+	0.286464i
$356$	18.8857	+	4.47599i	1.00094	+	0.237227i
$357$		0			0
$358$	1.11335	−	1.49549i	0.0588426	−	0.0790393i
$359$	27.1083	−	22.7466i	1.43072	−	1.20052i	0.485436	−	0.874272i	$-0.338661\pi$
$359$	27.1083	−	22.7466i	1.43072	−	1.20052i	0.945285	−	0.326245i	$-0.105784\pi$
$360$		0			0
$361$	0.352176	+	0.295511i	0.0185356	+	0.0155532i
$362$	−0.258380	+	0.0612372i	−0.0135802	+	0.00321856i
$363$		0			0
$364$	7.88512	+	5.18613i	0.413293	+	0.271827i
$365$	−45.4225	−	29.8748i	−2.37752	−	1.56372i
$366$		0			0
$367$	19.0674	−	4.51906i	0.995312	−	0.235893i	0.299484	−	0.954101i	$-0.403186\pi$
$367$	19.0674	−	4.51906i	0.995312	−	0.235893i	0.695828	+	0.718208i	$0.255037\pi$
$368$	3.19696	+	2.68257i	0.166653	+	0.139839i
$369$		0			0
$370$	1.02964	−	0.863973i	0.0535286	−	0.0449158i
$371$	−6.43236	+	8.64016i	−0.333952	+	0.448575i
$372$		0			0
$373$	31.5367	+	7.47433i	1.63291	+	0.387006i	0.941914	−	0.335854i	$-0.109025\pi$
$373$	31.5367	+	7.47433i	1.63291	+	0.387006i	0.690994	+	0.722860i	$0.257173\pi$
$374$	0.556320	+	0.747268i	0.0287666	+	0.0386403i
$375$		0			0
$376$	−4.20258	−	2.11062i	−0.216732	−	0.108847i
$377$	−1.14617	+	1.98523i	−0.0590309	+	0.102245i
$378$		0			0
$379$	7.22233	+	12.5094i	0.370986	+	0.642567i	0.989718	−	0.143036i	$-0.0456863\pi$
$379$	7.22233	+	12.5094i	0.370986	+	0.642567i	−0.618731	+	0.785603i	$0.712353\pi$
$380$	1.71566	+	29.4568i	0.0880115	+	1.51110i
$381$		0			0
$382$	2.56228	−	0.299487i	0.131098	−	0.0153231i
$383$	−6.27015	−	20.9437i	−0.320390	−	1.07018i	−0.954817	−	0.297193i	$-0.903949\pi$
$383$	−6.27015	−	20.9437i	−0.320390	−	1.07018i	0.634428	−	0.772982i	$-0.281236\pi$
$384$		0			0
$385$	−22.8013	−	52.8594i	−1.16206	−	2.69397i
$386$	1.64078	+	0.597194i	0.0835134	+	0.0303964i
$387$		0			0
$388$	−17.5223	+	6.37760i	−0.889561	+	0.323774i
$389$	−12.8716	−	13.6431i	−0.652617	−	0.691734i	0.313573	−	0.949564i	$-0.398474\pi$
$389$	−12.8716	−	13.6431i	−0.652617	−	0.691734i	−0.966190	+	0.257830i	$0.916992\pi$
$390$		0			0
$391$	−1.57165	+	0.789311i	−0.0794816	+	0.0399172i
$392$	−0.200702	+	3.44592i	−0.0101370	+	0.174045i
$393$		0			0
$394$	−0.0680719	+	0.227376i	−0.00342941	+	0.0114550i
$395$	−3.28846	+	18.6498i	−0.165461	+	0.938374i
$396$		0			0
$397$	−3.33925	−	18.9379i	−0.167592	−	0.950463i	−0.946351	−	0.323140i	$-0.895262\pi$
$397$	−3.33925	−	18.9379i	−0.167592	−	0.950463i	0.778759	−	0.627323i	$-0.215850\pi$
$398$	1.98107	+	0.231554i	0.0993019	+	0.0116067i
$399$		0			0
$400$	−17.0540	+	18.0762i	−0.852702	+	0.903811i
$401$	1.78850	−	4.14622i	0.0893137	−	0.207052i	−0.867704	−	0.497080i	$-0.834405\pi$
$401$	1.78850	−	4.14622i	0.0893137	−	0.207052i	0.957018	+	0.290028i	$0.0936647\pi$
$402$		0			0
$403$	7.20892	−	4.74138i	0.359102	−	0.236185i
$404$	−10.8668			−0.540643
$405$		0			0
$406$	−0.835597			−0.0414700
$407$	12.2820	−	8.07801i	0.608797	−	0.400412i
$408$		0			0
$409$	14.1854	−	32.8854i	0.701422	−	1.62608i	−0.0760060	−	0.997107i	$-0.524217\pi$
$409$	14.1854	−	32.8854i	0.701422	−	1.62608i	0.777428	−	0.628972i	$-0.216524\pi$
$410$	0.288843	−	0.306155i	0.0142649	−	0.0151199i
$411$		0			0
$412$	−4.62198	−	0.540232i	−0.227709	−	0.0266153i
$413$	−6.91757	−	39.2315i	−0.340392	−	1.93046i
$414$		0			0
$415$	−7.05659	+	40.0199i	−0.346395	+	1.96450i
$416$	−0.536452	+	1.79187i	−0.0263017	+	0.0878539i
$417$		0			0
$418$	0.145087	−	2.49105i	0.00709646	−	0.121841i
$419$	−22.2824	+	11.1906i	−1.08857	+	0.546698i	−0.900233	−	0.435408i	$-0.856604\pi$
$419$	−22.2824	+	11.1906i	−1.08857	+	0.546698i	−0.188332	+	0.982105i	$0.560308\pi$
$420$		0			0
$421$	24.7669	+	26.2513i	1.20706	+	1.27941i	0.949723	+	0.313092i	$0.101365\pi$
$421$	24.7669	+	26.2513i	1.20706	+	1.27941i	0.257340	+	0.966321i	$0.417154\pi$
$422$	0.449170	−	0.163485i	0.0218653	−	0.00795831i
$423$		0			0
$424$	−1.33566	−	0.486141i	−0.0648655	−	0.0236091i
$425$	−4.14806	−	9.61629i	−0.201211	−	0.466458i
$426$		0			0
$427$	5.69536	+	19.0238i	0.275618	+	0.920628i
$428$	−23.1966	+	2.71129i	−1.12125	+	0.131055i
$429$		0			0
$430$	−0.0559026	−	0.959810i	−0.00269586	−	0.0462862i
$431$	−12.8170	−	22.1998i	−0.617375	−	1.06933i	−0.989963	−	0.141329i	$-0.954863\pi$
$431$	−12.8170	−	22.1998i	−0.617375	−	1.06933i	0.372587	−	0.927997i	$-0.378471\pi$
$432$		0			0
$433$	−2.49590	+	4.32302i	−0.119945	+	0.207751i	−0.919746	−	0.392515i	$-0.871605\pi$
$433$	−2.49590	+	4.32302i	−0.119945	+	0.207751i	0.799801	+	0.600266i	$0.204939\pi$
$434$	2.81064	+	1.41156i	0.134915	+	0.0677570i
$435$		0			0
$436$	−0.502008	−	0.674313i	−0.0240418	−	0.0322937i
$437$	4.58366	+	1.08635i	0.219266	+	0.0519670i
$438$		0			0
$439$	2.00946	−	2.69917i	0.0959061	−	0.128824i	−0.751580	−	0.659642i	$-0.770708\pi$
$439$	2.00946	−	2.69917i	0.0959061	−	0.128824i	0.847486	+	0.530818i	$0.178115\pi$
$440$	5.81918	−	4.88287i	0.277418	−	0.232782i
$441$		0			0
$442$	−0.198684	−	0.166715i	−0.00945041	−	0.00792984i
$443$	13.0248	−	3.08693i	0.618825	−	0.146664i	0.0907666	−	0.995872i	$-0.471068\pi$
$443$	13.0248	−	3.08693i	0.618825	−	0.146664i	0.528059	+	0.849208i	$0.322920\pi$
$444$		0			0
$445$	27.5373	+	18.1116i	1.30540	+	0.858572i
$446$	0.309661	+	0.203667i	0.0146629	+	0.00964393i
$447$		0			0
$448$	27.7870	−	6.58564i	1.31281	−	0.311142i
$449$	25.1690	+	21.1193i	1.18780	+	0.996683i	0.999895	+	0.0144961i	$0.00461441\pi$
$449$	25.1690	+	21.1193i	1.18780	+	0.996683i	0.187906	+	0.982187i	$0.439830\pi$
$450$		0			0
$451$	3.52643	−	2.95903i	0.166053	−	0.139335i
$452$	−16.2708	+	21.8554i	−0.765313	+	1.02799i
$453$		0			0
$454$	2.89692	+	0.686582i	0.135959	+	0.0322229i
$455$	9.57062	+	12.8556i	0.448678	+	0.602679i
$456$		0			0
$457$	−18.9412	−	9.51261i	−0.886031	−	0.444981i	−0.0532479	−	0.998581i	$-0.516957\pi$
$457$	−18.9412	−	9.51261i	−0.886031	−	0.444981i	−0.832783	+	0.553600i	$0.813254\pi$
$458$	−0.293167	+	0.507780i	−0.0136988	+	0.0237270i
$459$		0			0
$460$	3.57135	+	6.18576i	0.166515	+	0.288413i
$461$	0.964285	+	16.5561i	0.0449112	+	0.771096i	0.943309	+	0.331914i	$0.107695\pi$
$461$	0.964285	+	16.5561i	0.0449112	+	0.771096i	−0.898398	+	0.439182i	$0.855268\pi$
$462$		0			0
$463$	−3.39720	+	0.397076i	−0.157881	+	0.0184537i	−0.194666	−	0.980870i	$-0.562362\pi$
$463$	−3.39720	+	0.397076i	−0.157881	+	0.0184537i	0.0367850	+	0.999323i	$0.488288\pi$
$464$	2.02119	+	6.75124i	0.0938313	+	0.313418i
$465$		0			0
$466$	−0.512771	−	1.18874i	−0.0237536	−	0.0550671i
$467$	−8.87582	−	3.23054i	−0.410724	−	0.149491i	0.128391	−	0.991724i	$-0.459019\pi$
$467$	−8.87582	−	3.23054i	−0.410724	−	0.149491i	−0.539115	+	0.842232i	$0.681241\pi$
$468$		0			0
$469$	−10.6895	+	3.89067i	−0.493597	+	0.179655i
$470$	−2.72967	−	2.89328i	−0.125910	−	0.133457i
$471$		0			0
$472$	4.69756	−	2.35921i	0.216223	−	0.108591i
$473$	0.611405	−	10.4974i	0.0281124	−	0.482672i
$474$		0			0
$475$	−8.04507	+	26.8724i	−0.369133	+	1.23299i
$476$	−2.12321	+	12.0413i	−0.0973173	+	0.551914i
$477$		0			0
$478$	−0.340467	−	1.93089i	−0.0155726	−	0.0883166i
$479$	18.1464	+	2.12101i	0.829130	+	0.0969114i	0.520062	−	0.854128i	$-0.325909\pi$
$479$	18.1464	+	2.12101i	0.829130	+	0.0969114i	0.309068	+	0.951040i	$0.399983\pi$
$480$		0			0
$481$	−2.80853	+	2.97687i	−0.128058	+	0.135734i
$482$	−0.865554	+	2.00658i	−0.0394249	+	0.0913972i
$483$		0			0
$484$	16.3335	−	10.7427i	0.742430	−	0.488304i
$485$	−31.6656			−1.43786
$486$		0			0
$487$	31.2157			1.41452			0.707260	−	0.706954i	$-0.249931\pi$
$487$	31.2157			1.41452			0.707260	+	0.706954i	$0.249931\pi$
$488$	−2.18931	+	1.43993i	−0.0991055	+	0.0651827i
$489$		0			0
$490$	−1.15638	+	2.68078i	−0.0522397	+	0.121105i
$491$	1.50047	−	1.59041i	0.0677154	−	0.0717741i	−0.692630	−	0.721293i	$-0.743548\pi$
$491$	1.50047	−	1.59041i	0.0677154	−	0.0717741i	0.760346	+	0.649519i	$0.225030\pi$
$492$		0			0
$493$	−2.94977	−	0.344779i	−0.132851	−	0.0155281i
$494$	0.120632	+	0.684137i	0.00542748	+	0.0307808i
$495$		0			0
$496$	4.60620	−	26.1231i	0.206825	−	1.17296i
$497$	2.14197	−	7.15469i	0.0960807	−	0.320932i
$498$		0			0
$499$	−0.0365869	+	0.628173i	−0.00163785	+	0.0281209i	−0.999028	−	0.0440786i	$-0.985965\pi$
$499$	−0.0365869	+	0.628173i	−0.00163785	+	0.0281209i	0.997390	+	0.0721995i	$0.0230018\pi$
$500$	−8.12227	+	4.07916i	−0.363239	+	0.182425i
$501$		0			0
$502$	1.75504	+	1.86024i	0.0783314	+	0.0830264i
$503$	−5.84089	+	2.12591i	−0.260432	+	0.0947897i	−0.468937	−	0.883232i	$-0.655363\pi$
$503$	−5.84089	+	2.12591i	−0.260432	+	0.0947897i	0.208504	+	0.978021i	$0.433141\pi$
$504$		0			0
$505$	−17.3408	−	6.31154i	−0.771656	−	0.280860i
$506$	−0.239245	−	0.554633i	−0.0106358	−	0.0246565i
$507$		0			0
$508$	2.06142	+	6.88562i	0.0914606	+	0.305500i
$509$	18.5886	−	2.17270i	0.823927	−	0.0963032i	0.306327	−	0.951926i	$-0.400900\pi$
$509$	18.5886	−	2.17270i	0.823927	−	0.0963032i	0.517600	+	0.855623i	$0.326826\pi$
$510$		0			0
$511$	3.50856	+	60.2396i	0.155209	+	2.66484i
$512$	4.80425	+	8.32121i	0.212320	+	0.367749i
$513$		0			0
$514$	−0.451387	+	0.781825i	−0.0199098	+	0.0344848i
$515$	−7.06180	−	3.54657i	−0.311180	−	0.156281i
$516$		0			0
$517$	−25.9789	−	34.8957i	−1.14255	−	1.53471i
$518$	−1.45162	−	0.344040i	−0.0637804	−	0.0151162i
$519$		0			0
$520$	−1.26290	+	1.69637i	−0.0553820	+	0.0743909i
$521$	10.7516	−	9.02171i	0.471038	−	0.395248i	−0.376135	−	0.926565i	$-0.622747\pi$
$521$	10.7516	−	9.02171i	0.471038	−	0.395248i	0.847173	+	0.531317i	$0.178303\pi$
$522$		0			0
$523$	−15.7777	−	13.2390i	−0.689910	−	0.578903i	0.228973	−	0.973433i	$-0.426463\pi$
$523$	−15.7777	−	13.2390i	−0.689910	−	0.578903i	−0.918883	+	0.394530i	$0.870908\pi$
$524$	−12.0693	+	2.86048i	−0.527251	+	0.124961i
$525$		0			0
$526$	1.08072	+	0.710799i	0.0471215	+	0.0309923i
$527$	9.33954	+	6.14271i	0.406837	+	0.267581i
$528$		0			0
$529$	−21.2705	+	5.04119i	−0.924803	+	0.219182i
$530$	−0.920961	−	0.772778i	−0.0400040	−	0.0335673i
$531$		0			0
$532$	25.0877	−	21.0511i	1.08769	−	0.912680i
$533$	−0.765321	+	1.02800i	−0.0331497	+	0.0445278i
$534$		0			0
$535$	−38.5909	−	9.14622i	−1.66843	−	0.395426i
$536$	−0.896382	−	1.20405i	−0.0387178	−	0.0520070i
$537$		0			0
$538$	2.47036	+	1.24066i	0.106505	+	0.0534888i
$539$	−15.9655	+	27.6531i	−0.687684	+	1.19110i
$540$		0			0
$541$	−19.2442	−	33.3319i	−0.827372	−	1.43305i	−0.900093	−	0.435698i	$-0.856502\pi$
$541$	−19.2442	−	33.3319i	−0.827372	−	1.43305i	0.0727213	−	0.997352i	$-0.476832\pi$
$542$	−0.167555	−	2.87681i	−0.00719711	−	0.123570i
$543$		0			0
$544$	−2.40689	+	0.281325i	−0.103194	+	0.0120617i
$545$	−0.409437	−	1.36761i	−0.0175383	−	0.0585821i
$546$		0			0
$547$	7.31275	+	16.9529i	0.312671	+	0.724852i	0.999999	−	0.00149506i	$-0.000475892\pi$
$547$	7.31275	+	16.9529i	0.312671	+	0.724852i	−0.687328	+	0.726347i	$0.741217\pi$
$548$	30.5412	+	11.1161i	1.30465	+	0.474855i
$549$		0			0
$550$	3.37997	−	1.23021i	0.144123	−	0.0524563i
$551$	5.45878	+	5.78597i	0.232552	+	0.246491i
$552$		0			0
$553$	18.7832	−	9.43326i	0.798741	−	0.401143i
$554$	0.0638278	−	1.09588i	0.00271178	−	0.0465595i
$555$		0			0
$556$	11.1236	−	37.1555i	0.471746	−	1.57574i
$557$	−1.24763	+	7.07568i	−0.0528639	+	0.299806i	−0.999764	−	0.0217217i	$-0.993085\pi$
$557$	−1.24763	+	7.07568i	−0.0528639	+	0.299806i	0.946900	+	0.321528i	$0.104196\pi$
$558$		0			0
$559$	0.508348	+	2.88298i	0.0215008	+	0.121937i
$560$	48.9380	+	5.72004i	2.06801	+	0.241716i
$561$		0			0
$562$	−1.82632	+	1.93578i	−0.0770386	+	0.0816561i
$563$	12.1926	−	28.2655i	0.513855	−	1.19125i	−0.441894	−	0.897067i	$-0.645693\pi$
$563$	12.1926	−	28.2655i	0.513855	−	1.19125i	0.955749	−	0.294183i	$-0.0950476\pi$
$564$		0			0
$565$	−38.6581	+	25.4258i	−1.62636	+	1.06967i
$566$	0.0757672			0.00318473
$567$		0			0
$568$	0.985508			0.0413510
$569$	−25.2451	+	16.6040i	−1.05833	+	0.696075i	−0.954407	−	0.298510i	$-0.903510\pi$
$569$	−25.2451	+	16.6040i	−1.05833	+	0.696075i	−0.103925	+	0.994585i	$0.533140\pi$
$570$		0			0
$571$	−3.12787	+	7.25122i	−0.130897	+	0.303454i	−0.971042	−	0.238908i	$-0.923211\pi$
$571$	−3.12787	+	7.25122i	−0.130897	+	0.303454i	0.840145	+	0.542362i	$0.182470\pi$
$572$	−7.90585	+	8.37972i	−0.330560	+	0.350374i
$573$		0			0
$574$	−0.464007	−	0.0542346i	−0.0193673	−	0.00226371i
$575$	1.17912	+	6.68713i	0.0491728	+	0.278873i
$576$		0			0
$577$	−1.81528	+	10.2950i	−0.0755710	+	0.428585i	0.923425	+	0.383780i	$0.125378\pi$
$577$	−1.81528	+	10.2950i	−0.0755710	+	0.428585i	−0.998996	+	0.0448050i	$0.985733\pi$
$578$	−0.507614	+	1.69555i	−0.0211139	+	0.0705255i
$579$		0			0
$580$	−0.701315	+	12.0411i	−0.0291205	+	0.499980i
$581$	40.3061	−	20.2425i	1.67218	−	0.839800i
$582$		0			0
$583$	−9.02322	−	9.56405i	−0.373703	−	0.396102i
$584$	−7.48227	+	2.72332i	−0.309619	+	0.112692i
$585$		0			0
$586$	−3.60373	−	1.31165i	−0.148869	−	0.0541837i
$587$	5.96314	+	13.8241i	0.246125	+	0.570582i	0.995834	−	0.0911857i	$-0.0290657\pi$
$587$	5.96314	+	13.8241i	0.246125	+	0.570582i	−0.749709	+	0.661768i	$0.769806\pi$
$588$		0			0
$589$	−8.58722	−	28.6833i	−0.353830	−	1.18188i
$590$	4.41615	−	0.516174i	0.181810	−	0.0212505i
$591$		0			0
$592$	0.731570	+	12.5606i	0.0300674	+	0.516237i
$593$	−9.50914	−	16.4703i	−0.390494	−	0.676355i	0.602021	−	0.798480i	$-0.294362\pi$
$593$	−9.50914	−	16.4703i	−0.390494	−	0.676355i	−0.992515	+	0.122125i	$0.961029\pi$
$594$		0			0
$595$	−10.3819	+	17.9819i	−0.425615	+	0.737187i
$596$	−7.26334	−	3.64779i	−0.297518	−	0.149419i
$597$		0			0
$598$	0.100421	+	0.134888i	0.00410651	+	0.00551600i
$599$	38.7477	+	9.18337i	1.58319	+	0.375222i	0.925704	−	0.378248i	$-0.123473\pi$
$599$	38.7477	+	9.18337i	1.58319	+	0.375222i	0.657482	+	0.753470i	$0.271621\pi$
$600$		0			0
$601$	3.33430	−	4.47874i	0.136009	−	0.182691i	−0.728901	−	0.684620i	$-0.759968\pi$
$601$	3.33430	−	4.47874i	0.136009	−	0.182691i	0.864909	+	0.501928i	$0.167376\pi$
$602$	−0.817450	+	0.685922i	−0.0333168	+	0.0279561i
$603$		0			0
$604$	−13.4821	−	11.3129i	−0.548580	−	0.460314i
$605$	32.3038	−	7.65613i	1.31333	−	0.311266i
$606$		0			0
$607$	−11.7624	−	7.73624i	−0.477420	−	0.314004i	0.287892	−	0.957663i	$-0.407045\pi$
$607$	−11.7624	−	7.73624i	−0.477420	−	0.314004i	−0.765313	+	0.643658i	$0.777416\pi$
$608$	5.42282	+	3.56665i	0.219925	+	0.144647i
$609$		0			0
$610$	−2.15663	+	0.511132i	−0.0873196	+	0.0206951i
$611$	9.27806	+	7.78522i	0.375350	+	0.314956i
$612$		0			0
$613$	−13.7550	+	11.5418i	−0.555561	+	0.466171i	−0.876819	−	0.480821i	$-0.840339\pi$
$613$	−13.7550	+	11.5418i	−0.555561	+	0.466171i	0.321258	+	0.946992i	$0.395894\pi$
$614$	−1.68287	+	2.26048i	−0.0679149	+	0.0912256i
$615$		0			0
$616$	−8.20403	−	1.94439i	−0.330550	−	0.0783417i
$617$	−20.4332	−	27.4466i	−0.822611	−	1.10496i	−0.992828	−	0.119552i	$-0.961854\pi$
$617$	−20.4332	−	27.4466i	−0.822611	−	1.10496i	0.170217	−	0.985407i	$-0.445553\pi$
$618$		0			0
$619$	−30.9588	−	15.5481i	−1.24434	−	0.624931i	−0.300012	−	0.953935i	$-0.596991\pi$
$619$	−30.9588	−	15.5481i	−1.24434	−	0.624931i	−0.944329	+	0.329004i	$0.893287\pi$
$620$	22.6998	−	39.3172i	0.911646	−	1.57902i
$621$		0			0
$622$	1.89740	+	3.28639i	0.0760787	+	0.131772i
$623$	−2.12706	−	36.5202i	−0.0852189	−	1.46315i
$624$		0			0
$625$	16.2488	−	1.89921i	0.649951	−	0.0759684i
$626$	−0.810406	−	2.70695i	−0.0323903	−	0.108191i
$627$		0			0
$628$	−4.16817	−	9.66290i	−0.166328	−	0.385592i
$629$	−4.98245	−	1.81347i	−0.198663	−	0.0723076i
$630$		0			0
$631$	40.5340	−	14.7532i	1.61363	−	0.587314i	0.631478	−	0.775394i	$-0.282449\pi$
$631$	40.5340	−	14.7532i	1.61363	−	0.587314i	0.982154	+	0.188080i	$0.0602263\pi$
$632$	1.90334	+	2.01742i	0.0757109	+	0.0802488i
$633$		0			0
$634$	−0.888066	+	0.446003i	−0.0352696	+	0.0177131i
$635$	−0.709701	+	12.1851i	−0.0281636	+	0.483551i
$636$		0			0
$637$	2.54959	−	8.51622i	0.101018	−	0.337425i
$638$	0.177121	−	1.00450i	0.00701230	−	0.0397687i
$639$		0			0
$640$	2.27566	+	12.9059i	0.0899534	+	0.510151i
$641$	4.77410	+	0.558012i	0.188566	+	0.0220402i	0.209851	−	0.977733i	$-0.432702\pi$
$641$	4.77410	+	0.558012i	0.188566	+	0.0220402i	−0.0212859	+	0.999773i	$0.506776\pi$
$642$		0			0
$643$	−5.69244	+	6.03363i	−0.224488	+	0.237943i	−0.829822	−	0.558028i	$-0.811558\pi$
$643$	−5.69244	+	6.03363i	−0.224488	+	0.237943i	0.605334	+	0.795971i	$0.293040\pi$
$644$	3.14002	−	7.27938i	0.123734	−	0.286848i
$645$		0			0
$646$	−0.751946	+	0.494563i	−0.0295849	+	0.0194583i
$647$	24.6332			0.968431			0.484215	−	0.874949i	$-0.339105\pi$
$647$	24.6332			0.968431			0.484215	+	0.874949i	$0.339105\pi$
$648$		0			0
$649$	48.6281			1.90882
$650$	−0.836644	+	0.550269i	−0.0328159	+	0.0215833i
$651$		0			0
$652$	3.82551	−	8.86852i	0.149818	−	0.347318i
$653$	7.36051	−	7.80169i	0.288039	−	0.305304i	−0.567155	−	0.823611i	$-0.691956\pi$
$653$	7.36051	−	7.80169i	0.288039	−	0.305304i	0.855195	+	0.518307i	$0.173438\pi$
$654$		0			0
$655$	−20.9212	−	2.44533i	−0.817458	−	0.0955471i
$656$	0.684175	+	3.88015i	0.0267125	+	0.151494i
$657$		0			0
$658$	−0.766638	+	4.34782i	−0.0298867	+	0.169496i
$659$	4.87841	−	16.2950i	0.190036	−	0.634764i	−0.808870	−	0.587988i	$-0.799920\pi$
$659$	4.87841	−	16.2950i	0.190036	−	0.634764i	0.998905	−	0.0467759i	$-0.0148947\pi$
$660$		0			0
$661$	1.81584	−	31.1767i	0.0706279	−	1.21263i	−0.757781	−	0.652509i	$-0.773716\pi$
$661$	1.81584	−	31.1767i	0.0706279	−	1.21263i	0.828409	−	0.560124i	$-0.189247\pi$
$662$	−2.03683	+	1.02294i	−0.0791638	+	0.0397575i
$663$		0			0
$664$	4.08431	+	4.32912i	0.158502	+	0.168002i
$665$	52.2606	−	19.0213i	2.02658	−	0.737615i
$666$		0			0
$667$	1.80945	+	0.658587i	0.0700622	+	0.0255006i
$668$	−17.5681	−	40.7275i	−0.679732	−	1.57580i
$669$		0			0
$670$	−0.364136	−	1.21630i	−0.0140678	−	0.0469897i
$671$	−24.0765	+	2.81415i	−0.929465	+	0.108639i
$672$		0			0
$673$	0.474625	+	8.14899i	0.0182954	+	0.314121i	0.995024	+	0.0996395i	$0.0317690\pi$
$673$	0.474625	+	8.14899i	0.0182954	+	0.314121i	−0.976728	+	0.214481i	$0.931194\pi$
$674$	1.65264	+	2.86245i	0.0636572	+	0.110258i
$675$		0			0
$676$	−11.2966	+	19.5663i	−0.434484	+	0.752548i
$677$	4.87031	+	2.44596i	0.187181	+	0.0940060i	0.539922	−	0.841715i	$-0.318454\pi$
$677$	4.87031	+	2.44596i	0.187181	+	0.0940060i	−0.352740	+	0.935721i	$0.614750\pi$
$678$		0			0
$679$	20.9877	+	28.1913i	0.805433	+	1.08188i
$680$	−2.66605	−	0.631866i	−0.102238	−	0.0242309i
$681$		0			0
$682$	−2.29266	+	3.07958i	−0.0877906	+	0.117923i
$683$	2.37757	−	1.99502i	0.0909753	−	0.0763374i	−0.596166	−	0.802861i	$-0.703310\pi$
$683$	2.37757	−	1.99502i	0.0909753	−	0.0763374i	0.687141	+	0.726524i	$0.258865\pi$
$684$		0			0
$685$	42.2801	+	35.4772i	1.61544	+	1.35551i
$686$	−0.00320928		0.000760612i	−0.000122531		2.90403e-5i
$687$		0			0
$688$	7.51923	+	4.94548i	0.286668	+	0.188544i
$689$	3.05842	+	2.01155i	0.116517	+	0.0766341i
$690$		0			0
$691$	24.6994	−	5.85387i	0.939610	−	0.222692i	0.267850	−	0.963461i	$-0.413687\pi$
$691$	24.6994	−	5.85387i	0.939610	−	0.222692i	0.671760	+	0.740769i	$0.265539\pi$
$692$	−5.30656	−	4.45274i	−0.201725	−	0.169268i
$693$		0			0
$694$	2.32850	−	1.95384i	0.0883885	−	0.0741667i
$695$	39.3309	−	52.8305i	1.49191	−	2.00398i
$696$		0			0
$697$	−1.61563	−	0.382911i	−0.0611964	−	0.0145038i
$698$	−1.24115	−	1.66716i	−0.0469784	−	0.0631029i
$699$		0			0
$700$	42.1866	+	21.1869i	1.59451	+	0.800791i
$701$	−0.473675	+	0.820430i	−0.0178905	+	0.0309872i	−0.874832	−	0.484426i	$-0.839028\pi$
$701$	−0.473675	+	0.820430i	−0.0178905	+	0.0309872i	0.856942	+	0.515414i	$0.172362\pi$
$702$		0			0
$703$	7.10086	+	12.2991i	0.267814	+	0.463868i
$704$	2.02686	+	34.7998i	0.0763901	+	1.31157i
$705$		0			0
$706$	−2.42080	+	0.282951i	−0.0911080	+	0.0106490i
$707$	5.87427	+	19.6214i	0.220925	+	0.737940i
$708$		0			0
$709$	12.7765	+	29.6192i	0.479831	+	1.11237i	0.970516	+	0.241036i	$0.0774871\pi$
$709$	12.7765	+	29.6192i	0.479831	+	1.11237i	−0.490686	+	0.871337i	$0.663254\pi$
$710$	0.783290	+	0.285094i	0.0293963	+	0.0106994i
$711$		0			0
$712$	4.53612	−	1.65101i	0.169998	−	0.0618743i
$713$	−4.97380	−	5.27192i	−0.186270	−	0.197435i
$714$		0			0
$715$	−17.4829	+	8.78023i	−0.653822	+	0.328362i
$716$	−1.73679	+	29.8195i	−0.0649068	+	1.11441i
$717$		0			0
$718$	1.25726	−	4.19954i	0.0469206	−	0.156726i
$719$	4.35548	−	24.7012i	0.162432	−	0.921198i	−0.789241	−	0.614084i	$-0.789526\pi$
$719$	4.35548	−	24.7012i	0.162432	−	0.921198i	0.951673	−	0.307114i	$-0.0993633\pi$
$720$		0			0
$721$	1.52305	+	8.63763i	0.0567213	+	0.321682i
$722$	0.0565657	+	0.00661158i	0.00210516	+	0.000246057i
$723$		0			0
$724$	2.91941	−	3.09440i	0.108499	−	0.115002i
$725$	−4.54162	+	10.5287i	−0.168671	+	0.391024i
$726$		0			0
$727$	7.26093	−	4.77559i	0.269293	−	0.177117i	−0.407680	−	0.913125i	$-0.633662\pi$
$727$	7.26093	−	4.77559i	0.269293	−	0.177117i	0.676973	+	0.736008i	$0.263292\pi$
$728$	2.34729			0.0869964
$729$		0			0
$730$	−6.73479			−0.249266
$731$	−3.16873	+	2.08411i	−0.117200	+	0.0770836i
$732$		0			0
$733$	3.43532	−	7.96396i	0.126886	−	0.294156i	−0.842917	−	0.538043i	$-0.819164\pi$
$733$	3.43532	−	7.96396i	0.126886	−	0.294156i	0.969803	+	0.243888i	$0.0784229\pi$
$734$	1.66583	−	1.76567i	0.0614867	−	0.0651721i
$735$		0			0
$736$	1.56056	+	0.182404i	0.0575231	+	0.00672349i
$737$	−2.41128	−	13.6750i	−0.0888205	−	0.503726i
$738$		0			0
$739$	−0.311908	+	1.76892i	−0.0114737	+	0.0650707i	−0.990007	−	0.141018i	$-0.954962\pi$
$739$	−0.311908	+	1.76892i	−0.0114737	+	0.0650707i	0.978533	+	0.206089i	$0.0660736\pi$
$740$	−6.17602	+	20.6293i	−0.227035	+	0.758349i
$741$		0			0
$742$	−0.0775863	+	1.33211i	−0.00284828	+	0.0489031i
$743$	−20.8516	+	10.4721i	−0.764972	+	0.384183i	−0.788098	−	0.615549i	$-0.788934\pi$
$743$	−20.8516	+	10.4721i	−0.764972	+	0.384183i	0.0231267	+	0.999733i	$0.492638\pi$
$744$		0			0
$745$	−9.47189	−	10.0396i	−0.347023	−	0.367823i
$746$	3.77279	−	1.37318i	0.138132	−	0.0502758i
$747$		0			0
$748$	−14.0253	−	5.10480i	−0.512816	−	0.186650i
$749$	17.4350	+	40.4189i	0.637061	+	1.47687i
$750$		0			0
$751$	−5.56559	−	18.5904i	−0.203091	−	0.678373i	−0.997479	−	0.0709615i	$-0.977393\pi$
$751$	−5.56559	−	18.5904i	−0.203091	−	0.678373i	0.794388	−	0.607411i	$-0.207792\pi$
$752$	36.9828	−	4.32267i	1.34862	−	0.157631i
$753$		0			0
$754$	0.0165114	+	0.283490i	0.000601310	+	0.0103241i
$755$	−14.9437	−	25.8832i	−0.543855	−	0.941985i
$756$		0			0
$757$	−8.52025	+	14.7575i	−0.309674	+	0.536371i	−0.978291	−	0.207236i	$-0.933553\pi$
$757$	−8.52025	+	14.7575i	−0.309674	+	0.536371i	0.668617	+	0.743607i	$0.266886\pi$
$758$	1.59904	+	0.803069i	0.0580798	+	0.0291688i
$759$		0			0
$760$	4.38237	+	5.88654i	0.158965	+	0.213527i
$761$	−41.7260	−	9.88923i	−1.51256	−	0.358484i	−0.611176	−	0.791495i	$-0.709303\pi$
$761$	−41.7260	−	9.88923i	−1.51256	−	0.358484i	−0.901389	+	0.433011i	$0.857451\pi$
$762$		0			0
$763$	−0.946191	+	1.27096i	−0.0342544	+	0.0460117i
$764$	−31.6606	+	26.5664i	−1.14544	+	0.961137i
$765$		0			0
$766$	−2.07463	−	1.74082i	−0.0749594	−	0.0628984i
$767$	−13.1732	+	3.12212i	−0.475658	+	0.112733i
$768$		0			0
$769$	−23.8376	−	15.6782i	−0.859605	−	0.565371i	0.0414182	−	0.999142i	$-0.486812\pi$
$769$	−23.8376	−	15.6782i	−0.859605	−	0.565371i	−0.901023	+	0.433771i	$0.857183\pi$
$770$	−5.95814	−	3.91873i	−0.214716	−	0.141221i
$771$		0			0
$772$	−27.2200	+	6.45127i	−0.979671	+	0.232186i
$773$	−31.5157	−	26.4448i	−1.13354	−	0.951155i	−0.134334	−	0.990936i	$-0.542889\pi$
$773$	−31.5157	−	26.4448i	−1.13354	−	0.951155i	−0.999208	+	0.0397813i	$0.987334\pi$
$774$		0			0
$775$	33.0622	−	27.7425i	1.18763	−	0.996539i
$776$	−2.76945	+	3.72002i	−0.0994176	+	0.133541i
$777$		0			0
$778$	−2.26090	−	0.535844i	−0.0810573	−	0.0192109i
$779$	2.65572	+	3.56725i	0.0951511	+	0.127810i
$780$		0			0
$781$	8.14691	+	4.09153i	0.291519	+	0.146406i
$782$	−0.108933	+	0.188677i	−0.00389543	+	0.00674709i
$783$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.103498 - 0.0680719i) q^{2} +(-0.786081 + 1.82234i) q^{4} +(-2.31283 + 2.45146i) q^{5} +(3.71541 + 0.434269i) q^{7} +(0.0857144 + 0.486111i) q^{8} +O(q^{10})\)	\(q+(0.103498 - 0.0680719i) q^{2} +(-0.786081 + 1.82234i) q^{4} +(-2.31283 + 2.45146i) q^{5} +(3.71541 + 0.434269i) q^{7} +(0.0857144 + 0.486111i) q^{8} +(-0.0724987 + 0.411161i) q^{10} +(-1.30961 + 4.37439i) q^{11} +(0.0739164 - 1.26910i) q^{13} +(0.414100 - 0.207969i) q^{14} +(-2.68194 - 2.84269i) q^{16} +(1.54764 - 0.563296i) q^{17} +(-4.14528 - 1.50876i) q^{19} +(-2.64932 - 6.14181i) q^{20} +(0.162231 + 0.541890i) q^{22} +(-1.06063 + 0.123970i) q^{23} +(-0.369733 - 6.34808i) q^{25} +(-0.0787396 - 0.136381i) q^{26} +(-3.71200 + 6.42938i) q^{28} +(-1.61142 - 0.809287i) q^{29} +(4.05312 + 5.44429i) q^{31} +(-1.43169 - 0.339317i) q^{32} +(0.121834 - 0.163651i) q^{34} +(-9.65772 + 8.10379i) q^{35} +(-2.46619 - 2.06938i) q^{37} +(-0.531734 + 0.126023i) q^{38} +(-1.38992 - 0.914167i) q^{40} +(-0.842295 - 0.553986i) q^{41} +(-2.24075 + 0.531068i) q^{43} +(-6.94218 - 5.82518i) q^{44} +(-0.101335 + 0.0850299i) q^{46} +(-5.68936 + 7.64213i) q^{47} +(6.80439 + 1.61267i) q^{49} +(-0.470392 - 0.631847i) q^{50} +(2.25462 + 1.13231i) q^{52} +(-1.43978 + 2.49378i) q^{53} +(-7.69474 - 13.3277i) q^{55} +(0.107361 + 1.84333i) q^{56} +(-0.221869 + 0.0259328i) q^{58} +(-3.05432 - 10.2021i) q^{59} +(2.10265 + 4.87448i) q^{61} +(0.790095 + 0.287571i) q^{62} +(7.17367 - 2.61100i) q^{64} +(2.94018 + 3.11641i) q^{65} +(-2.71756 + 1.36481i) q^{67} +(-0.190056 + 3.26313i) q^{68} +(-0.447917 + 1.49615i) q^{70} +(0.346694 - 1.96620i) q^{71} +(2.80114 + 15.8860i) q^{73} +(-0.396113 - 0.0462990i) q^{74} +(6.00801 - 6.36811i) q^{76} +(-6.76540 + 15.6840i) q^{77} +(4.69457 - 3.08767i) q^{79} +13.1716 q^{80} -0.124887 q^{82} +(10.0739 - 6.62572i) q^{83} +(-2.19854 + 5.09679i) q^{85} +(-0.195763 + 0.207497i) q^{86} +(-2.23869 - 0.261666i) q^{88} +(-1.69819 - 9.63089i) q^{89} +(0.825760 - 4.68312i) q^{91} +(0.607827 - 2.03028i) q^{92} +(-0.0686242 + 1.17823i) q^{94} +(13.2860 - 6.67248i) q^{95} +(6.44760 + 6.83405i) q^{97} +(0.814020 - 0.296279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more