LMFDB - Embedded newform 729.2.g.d.28.4

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			28.4
Character	$\chi$	$=$	729.28
Dual form			729.2.g.d.703.4

$q$-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	−0.585574	−	0.810619i	$-0.699131\pi$
$2$	−0.103498	+	0.0680719i	−0.0731843	+	0.0481341i	0.512390	+	0.858753i	$0.328760\pi$
$3$		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	$-0.487566\pi$
$5$	2.31283	−	2.45146i	1.03433	−	1.09633i	0.995276	−	0.0970882i	$-0.0309529\pi$
$6$		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	$-0.665728\pi$
$11$	1.30961	−	4.37439i	0.394861	−	1.31893i	0.892305	−	0.451433i	$-0.149087\pi$
$12$		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	−0.522808	−	0.852450i	$-0.675116\pi$
$17$	−1.54764	+	0.563296i	−0.375359	+	0.136619i	0.147450	+	0.989070i	$0.452893\pi$
$18$		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	−0.00479276	−	0.999989i	$-0.501526\pi$
$23$	1.06063	−	0.123970i	0.221157	−	0.0258495i	0.225950	+	0.974139i	$0.427452\pi$
$24$		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	0.592081	−	0.805878i	$-0.298307\pi$
$29$	1.61142	+	0.809287i	0.299234	+	0.150281i	−0.292847	+	0.956159i	$0.594603\pi$
$30$		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	0.613576	−	0.789636i	$-0.289731\pi$
$41$	0.842295	+	0.553986i	0.131544	+	0.0865181i	−0.482031	+	0.876154i	$0.660101\pi$
$42$		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	$-0.551765\pi$
$47$	5.68936	−	7.64213i	0.829878	−	1.11472i	0.991785	−	0.127913i	$-0.0408280\pi$
$48$		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	−0.750035	−	0.661398i	$-0.769964\pi$
$53$	1.43978	−	2.49378i	0.197769	−	0.342547i	0.947805	+	0.318851i	$0.103297\pi$
$54$		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	$0.151218\pi$
$59$	3.05432	+	10.2021i	0.397638	+	1.32820i	−0.491625	+	0.870807i	$0.663597\pi$
$60$		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	−0.998445	−	0.0557526i	$-0.982244\pi$
$71$	−0.346694	+	1.96620i	−0.0411451	+	0.233345i	0.957300	+	0.289098i	$0.0933553\pi$
$72$		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	−0.964862	−	0.262758i	$-0.915368\pi$
$83$	−10.0739	+	6.62572i	−1.10576	+	0.727267i	−0.140894	+	0.990025i	$0.544998\pi$
$84$		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	$0.117883\pi$
$89$	1.69819	+	9.63089i	0.180007	+	1.02087i	−0.752197	+	0.658939i	$0.771006\pi$
$90$		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	0.775593	−	0.631233i	$-0.217451\pi$
$101$	−2.16870	−	5.02761i	−0.215794	−	0.500266i	−0.991387	+	0.130967i	$0.958192\pi$
$102$		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	$-0.974072\pi$
$107$	−5.88377	−	10.1910i	−0.568805	−	0.985200i	0.427879	−	0.903836i	$-0.359261\pi$
$108$		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	−0.452257	−	0.891888i	$-0.649381\pi$
$113$	−13.3588	−	3.16609i	−1.25669	−	0.297840i	−0.804430	+	0.594047i	$0.797529\pi$
$114$		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	0.608610	−	0.793469i	$-0.291727\pi$
$131$	−3.73212	−	5.01310i	−0.326077	−	0.437997i	−0.934687	+	0.355473i	$0.884320\pi$
$132$		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	$0.228102\pi$
$137$	0.952195	+	16.3486i	0.0813515	+	1.39675i	−0.672690	+	0.739925i	$0.734861\pi$
$138$		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	$-0.927830\pi$
$149$	0.238124	−	4.08844i	0.0195079	−	0.334938i	0.993915	−	0.110148i	$-0.0351325\pi$
$150$		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	$-0.426762\pi$
$167$	15.3368	−	16.2561i	1.18680	−	1.25793i	0.958739	−	0.284286i	$-0.0917566\pi$
$168$		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	−0.911465	−	0.411378i	$-0.865048\pi$
$173$	1.00106	−	3.34376i	0.0761089	−	0.254221i	0.987574	+	0.157157i	$0.0502328\pi$
$174$		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	−0.811332	−	0.584585i	$-0.801257\pi$
$179$	−14.1428	+	5.14757i	−1.05709	+	0.384748i	−0.245753	+	0.969333i	$0.579035\pi$
$180$		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	−0.378168	−	0.925737i	$-0.623446\pi$
$191$	−18.6097	−	9.34613i	−1.34655	−	0.676262i	−0.968381	+	0.249475i	$0.919742\pi$
$192$		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	−0.589003	−	0.808131i	$-0.700479\pi$
$197$	1.46772	−	1.23157i	0.104571	−	0.0877455i	0.693574	+	0.720385i	$0.256035\pi$
$198$		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	$-0.946861\pi$
$227$	−16.4925	−	17.4810i	−1.09465	−	1.16026i	−0.108549	−	0.994091i	$-0.534620\pi$
$228$		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	$0.166770\pi$
$233$	−1.81475	+	10.2920i	−0.118888	+	0.674250i	−0.984751	+	0.173968i	$0.944341\pi$
$234$		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	$0.300687\pi$
$239$	−6.26895	+	14.5331i	−0.405504	+	0.940065i	−0.991543	+	0.129782i	$0.958572\pi$
$240$		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	$-0.829673\pi$
$251$	−3.58499	−	20.3315i	−0.226282	−	1.28331i	0.633936	−	0.773386i	$-0.281438\pi$
$252$		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	−0.233934	−	0.972252i	$-0.575160\pi$
$257$	6.51246	−	3.27068i	0.406236	−	0.204019i	0.640170	+	0.768233i	$0.278864\pi$
$258$		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	0.741818	−	0.670601i	$-0.233964\pi$
$263$	−4.13582	−	9.58791i	−0.255026	−	0.591216i	−0.996844	+	0.0793849i	$0.974704\pi$
$264$		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	$-0.928515\pi$
$269$	−11.1578	−	19.3259i	−0.680304	−	1.17832i	0.294585	−	0.955625i	$-0.404819\pi$
$270$		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	0.446483	−	0.894792i	$-0.352676\pi$
$281$	20.9045	−	4.95445i	1.24706	−	0.295558i	0.800574	+	0.599234i	$0.204528\pi$
$282$		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	$0.155897\pi$
$293$	18.4868	+	24.8321i	1.08001	+	1.45071i	0.197569	+	0.980289i	$0.436695\pi$
$294$		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	$-0.646547\pi$
$311$	1.78117	−	30.5816i	0.101001	−	1.73412i	0.545299	−	0.838242i	$-0.316416\pi$
$312$		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	0.336871	−	0.941551i	$-0.390631\pi$
$317$	7.96795	+	0.931320i	0.447525	+	0.0523081i	0.110654	+	0.993859i	$0.464706\pi$
$318$		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	−0.741522	−	0.670929i	$-0.765896\pi$
$347$	−24.3715	+	2.84862i	−1.30833	+	0.152922i	−0.566807	+	0.823850i	$0.691822\pi$
$348$		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	0.850263	−	0.526357i	$-0.176443\pi$
$353$	17.5821	+	8.83007i	0.935802	+	0.469977i	0.0855386	+	0.996335i	$0.472739\pi$
$354$		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	$0.661339\pi$
$359$	−27.1083	+	22.7466i	−1.43072	+	1.20052i	−0.945285	+	0.326245i	$0.894216\pi$
$360$		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	$0.0960506\pi$
$383$	6.27015	+	20.9437i	0.320390	+	1.07018i	−0.634428	+	0.772982i	$0.718764\pi$
$384$		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	0.966190	−	0.257830i	$-0.0830076\pi$
$389$	12.8716	+	13.6431i	0.652617	+	0.691734i	−0.313573	+	0.949564i	$0.601526\pi$
$390$		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	−0.957018	−	0.290028i	$-0.906335\pi$
$401$	−1.78850	+	4.14622i	−0.0893137	+	0.207052i	0.867704	+	0.497080i	$0.165595\pi$
$402$		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	0.188332	−	0.982105i	$-0.439692\pi$
$419$	22.2824	−	11.1906i	1.08857	−	0.546698i	0.900233	+	0.435408i	$0.143396\pi$
$420$		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	$0.0451374\pi$
$431$	12.8170	+	22.1998i	0.617375	+	1.06933i	−0.372587	+	0.927997i	$0.621529\pi$
$432$		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	−0.528059	−	0.849208i	$-0.677080\pi$
$443$	−13.0248	+	3.08693i	−0.618825	+	0.146664i	−0.0907666	+	0.995872i	$0.528932\pi$
$444$		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	$-0.995386\pi$
$449$	−25.1690	−	21.1193i	−1.18780	−	0.996683i	−0.187906	−	0.982187i	$-0.560170\pi$
$450$		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	$-0.892305\pi$
$461$	−0.964285	−	16.5561i	−0.0449112	−	0.771096i	0.898398	−	0.439182i	$-0.144732\pi$
$462$		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	0.539115	−	0.842232i	$-0.318759\pi$
$467$	8.87582	+	3.23054i	0.410724	+	0.149491i	−0.128391	+	0.991724i	$0.540981\pi$
$468$		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	−0.309068	−	0.951040i	$-0.600017\pi$
$479$	−18.1464	−	2.12101i	−0.829130	−	0.0969114i	−0.520062	+	0.854128i	$0.674091\pi$
$480$		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	−0.760346	−	0.649519i	$-0.774970\pi$
$491$	−1.50047	+	1.59041i	−0.0677154	+	0.0717741i	0.692630	+	0.721293i	$0.256452\pi$
$492$		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	−0.208504	−	0.978021i	$-0.566859\pi$
$503$	5.84089	−	2.12591i	0.260432	−	0.0947897i	0.468937	+	0.883232i	$0.344637\pi$
$504$		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	−0.517600	−	0.855623i	$-0.673174\pi$
$509$	−18.5886	+	2.17270i	−0.823927	+	0.0963032i	−0.306327	+	0.951926i	$0.599100\pi$
$510$		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	−0.847173	−	0.531317i	$-0.821697\pi$
$521$	−10.7516	+	9.02171i	−0.471038	+	0.395248i	0.376135	+	0.926565i	$0.377253\pi$
$522$		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	−0.946900	−	0.321528i	$-0.895804\pi$
$557$	1.24763	−	7.07568i	0.0528639	−	0.299806i	0.999764	+	0.0217217i	$0.00691477\pi$
$558$		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	$0.354307\pi$
$563$	−12.1926	+	28.2655i	−0.513855	+	1.19125i	−0.955749	+	0.294183i	$0.904952\pi$
$564$		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	0.103925	−	0.994585i	$-0.466860\pi$
$569$	25.2451	−	16.6040i	1.05833	−	0.696075i	0.954407	+	0.298510i	$0.0964896\pi$
$570$		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	0.749709	−	0.661768i	$-0.230194\pi$
$587$	−5.96314	−	13.8241i	−0.246125	−	0.570582i	−0.995834	+	0.0911857i	$0.970934\pi$
$588$		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	0.992515	−	0.122125i	$-0.0389710\pi$
$593$	9.50914	+	16.4703i	0.390494	+	0.676355i	−0.602021	+	0.798480i	$0.705638\pi$
$594$		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	−0.657482	−	0.753470i	$-0.728379\pi$
$599$	−38.7477	−	9.18337i	−1.58319	−	0.375222i	−0.925704	+	0.378248i	$0.876527\pi$
$600$		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	$0.0381458\pi$
$617$	20.4332	+	27.4466i	0.822611	+	1.10496i	−0.170217	+	0.985407i	$0.554447\pi$
$618$		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	0.0212859	−	0.999773i	$-0.493224\pi$
$641$	−4.77410	−	0.558012i	−0.188566	−	0.0220402i	−0.209851	+	0.977733i	$0.567298\pi$
$642$		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	$-0.660895\pi$
$647$	−24.6332			−0.968431			−0.484215	+	0.874949i	$0.660895\pi$
$648$		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	−0.855195	−	0.518307i	$-0.826562\pi$
$653$	−7.36051	+	7.80169i	−0.288039	+	0.305304i	0.567155	+	0.823611i	$0.308044\pi$
$654$		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	$0.200080\pi$
$659$	−4.87841	+	16.2950i	−0.190036	+	0.634764i	−0.998905	+	0.0467759i	$0.985105\pi$
$660$		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	0.352740	−	0.935721i	$-0.385250\pi$
$677$	−4.87031	−	2.44596i	−0.187181	−	0.0940060i	−0.539922	+	0.841715i	$0.681546\pi$
$678$		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	−0.687141	−	0.726524i	$-0.741135\pi$
$683$	−2.37757	+	1.99502i	−0.0909753	+	0.0763374i	0.596166	+	0.802861i	$0.296690\pi$
$684$		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	−0.856942	−	0.515414i	$-0.827638\pi$
$701$	0.473675	−	0.820430i	0.0178905	−	0.0309872i	0.874832	+	0.484426i	$0.160972\pi$
$702$		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	$0.210474\pi$
$719$	−4.35548	+	24.7012i	−0.162432	+	0.921198i	−0.951673	+	0.307114i	$0.900637\pi$
$720$		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	−0.0231267	−	0.999733i	$-0.507362\pi$
$743$	20.8516	−	10.4721i	0.764972	−	0.384183i	0.788098	+	0.615549i	$0.211066\pi$
$744$		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	0.901389	−	0.433011i	$-0.142549\pi$
$761$	41.7260	+	9.88923i	1.51256	+	0.358484i	0.611176	+	0.791495i	$0.290697\pi$
$762$		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	0.999208	−	0.0397813i	$-0.0126661\pi$
$773$	31.5157	+	26.4448i	1.13354	+	0.951155i	0.134334	+	0.990936i	$0.457111\pi$
$774$		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

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