LMFDB - Embedded newform 729.2.g.d.703.4

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			703.4
Character	$\chi$	$=$	729.703
Dual form			729.2.g.d.28.4

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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	$-0.328760\pi$
$2$	−0.103498	−	0.0680719i	−0.0731843	−	0.0481341i	−0.585574	+	0.810619i	$0.699131\pi$
$3$		0			0
$3$		0			0
$4$	−0.786081	−	1.82234i	−0.393041	−	0.911171i
$5$	2.31283	+	2.45146i	1.03433	+	1.09633i	0.995276	+	0.0970882i	$0.0309529\pi$
$5$	2.31283	+	2.45146i	1.03433	+	1.09633i	0.0390538	+	0.999237i	$0.487566\pi$
$6$		0			0
$7$	3.71541	−	0.434269i	1.40429	−	0.164138i	0.620036	−	0.784573i	$-0.287118\pi$
$7$	3.71541	−	0.434269i	1.40429	−	0.164138i	0.784258	+	0.620435i	$0.213044\pi$
$8$	−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	0.892305	+	0.451433i	$0.149087\pi$
$11$	1.30961	+	4.37439i	0.394861	+	1.31893i	−0.497444	+	0.867496i	$0.665728\pi$
$12$		0			0
$13$	0.0739164	+	1.26910i	0.0205007	+	0.351984i	0.992923	+	0.118758i	$0.0378912\pi$
$13$	0.0739164	+	1.26910i	0.0205007	+	0.351984i	−0.972423	+	0.233226i	$0.925072\pi$
$14$	−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	$-0.452893\pi$
$17$	−1.54764	−	0.563296i	−0.375359	−	0.136619i	−0.522808	+	0.852450i	$0.675116\pi$
$18$		0			0
$19$	−4.14528	+	1.50876i	−0.950993	+	0.346133i	−0.770498	−	0.637443i	$-0.779992\pi$
$19$	−4.14528	+	1.50876i	−0.950993	+	0.346133i	−0.180495	+	0.983576i	$0.557770\pi$
$20$	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	$-0.427452\pi$
$23$	1.06063	+	0.123970i	0.221157	+	0.0258495i	−0.00479276	+	0.999989i	$0.501526\pi$
$24$		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	$-0.594603\pi$
$29$	1.61142	−	0.809287i	0.299234	−	0.150281i	0.592081	+	0.805878i	$0.298307\pi$
$30$		0			0
$31$	4.05312	−	5.44429i	0.727963	−	0.977823i	−0.271917	−	0.962321i	$-0.587658\pi$
$31$	4.05312	−	5.44429i	0.727963	−	0.977823i	0.999880	−	0.0155028i	$-0.00493490\pi$
$32$	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	−0.822592	−	0.568633i	$-0.807473\pi$
$37$	−2.46619	+	2.06938i	−0.405439	+	0.340204i	0.417152	+	0.908837i	$0.363028\pi$
$38$	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	$-0.660101\pi$
$41$	0.842295	−	0.553986i	0.131544	−	0.0865181i	0.613576	+	0.789636i	$0.289731\pi$
$42$		0			0
$43$	−2.24075	−	0.531068i	−0.341711	−	0.0809871i	0.0561773	−	0.998421i	$-0.482109\pi$
$43$	−2.24075	−	0.531068i	−0.341711	−	0.0809871i	−0.397889	+	0.917434i	$0.630257\pi$
$44$	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	0.991785	+	0.127913i	$0.0408280\pi$
$47$	5.68936	+	7.64213i	0.829878	+	1.11472i	−0.161908	+	0.986806i	$0.551765\pi$
$48$		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	$-0.103297\pi$
$53$	1.43978	+	2.49378i	0.197769	+	0.342547i	−0.750035	+	0.661398i	$0.769964\pi$
$54$		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	−0.491625	−	0.870807i	$-0.663597\pi$
$59$	3.05432	−	10.2021i	0.397638	−	1.32820i	0.889263	−	0.457397i	$-0.151218\pi$
$60$		0			0
$61$	2.10265	−	4.87448i	0.269216	−	0.624114i	−0.728955	−	0.684562i	$-0.759994\pi$
$61$	2.10265	−	4.87448i	0.269216	−	0.624114i	0.998171	+	0.0604479i	$0.0192529\pi$
$62$	−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	0.274987	−	0.961448i	$-0.411327\pi$
$67$	−2.71756	−	1.36481i	−0.332002	−	0.166738i	−0.606989	+	0.794710i	$0.707623\pi$
$68$	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	$-0.0933553\pi$
$71$	−0.346694	−	1.96620i	−0.0411451	−	0.233345i	−0.998445	+	0.0557526i	$0.982244\pi$
$72$		0			0
$73$	2.80114	−	15.8860i	0.327848	−	1.85932i	−0.161006	−	0.986953i	$-0.551474\pi$
$73$	2.80114	−	15.8860i	0.327848	−	1.85932i	0.488854	−	0.872366i	$-0.337415\pi$
$74$	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	0.785425	−	0.618956i	$-0.212444\pi$
$79$	4.69457	+	3.08767i	0.528181	+	0.347390i	−0.257245	+	0.966346i	$0.582815\pi$
$80$	−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	$-0.544998\pi$
$83$	−10.0739	−	6.62572i	−1.10576	−	0.727267i	−0.964862	+	0.262758i	$0.915368\pi$
$84$		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	−0.752197	−	0.658939i	$-0.771006\pi$
$89$	1.69819	−	9.63089i	0.180007	−	1.02087i	0.932204	−	0.361934i	$-0.117883\pi$
$90$		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	−0.311970	−	0.950092i	$-0.600989\pi$
$97$	6.44760	−	6.83405i	0.654654	−	0.693893i	0.966624	+	0.256199i	$0.0824702\pi$
$98$	−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	$-0.958192\pi$
$101$	−2.16870	+	5.02761i	−0.215794	+	0.500266i	0.775593	+	0.631233i	$0.217451\pi$
$102$		0			0
$103$	0.672471	−	2.24621i	0.0662606	−	0.221326i	−0.918446	−	0.395546i	$-0.870555\pi$
$103$	0.672471	−	2.24621i	0.0662606	−	0.221326i	0.984707	+	0.174220i	$0.0557405\pi$
$104$	−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	0.427879	+	0.903836i	$0.359261\pi$
$107$	−5.88377	+	10.1910i	−0.568805	+	0.985200i	−0.996684	+	0.0813640i	$0.974072\pi$
$108$		0			0
$109$	−0.211790	−	0.366831i	−0.0202858	−	0.0351361i	0.855704	−	0.517465i	$-0.173124\pi$
$109$	−0.211790	−	0.366831i	−0.0202858	−	0.0351361i	−0.875990	+	0.482329i	$0.839791\pi$
$110$	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	$-0.797529\pi$
$113$	−13.3588	+	3.16609i	−1.25669	+	0.297840i	−0.452257	+	0.891888i	$0.649381\pi$
$114$		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	0.757524	−	0.652807i	$-0.226409\pi$
$127$	2.77429	+	2.32790i	0.246178	+	0.206568i	−0.511346	+	0.859375i	$0.670853\pi$
$128$	−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	$-0.884320\pi$
$131$	−3.73212	+	5.01310i	−0.326077	+	0.437997i	0.608610	+	0.793469i	$0.291727\pi$
$132$		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	−0.672690	−	0.739925i	$-0.734861\pi$
$137$	0.952195	−	16.3486i	0.0813515	−	1.39675i	0.754041	−	0.656827i	$-0.228102\pi$
$138$		0			0
$139$	−19.4102	−	2.26873i	−1.64635	−	0.192431i	−0.758214	−	0.652006i	$-0.773928\pi$
$139$	−19.4102	−	2.26873i	−1.64635	−	0.192431i	−0.888139	+	0.459574i	$0.848002\pi$
$140$	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	0.993915	+	0.110148i	$0.0351325\pi$
$149$	0.238124	+	4.08844i	0.0195079	+	0.334938i	−0.974407	+	0.224790i	$0.927830\pi$
$150$		0			0
$151$	−2.54334	−	8.49534i	−0.206974	−	0.691341i	−0.996939	−	0.0781885i	$-0.975086\pi$
$151$	−2.54334	−	8.49534i	−0.206974	−	0.691341i	0.789965	−	0.613152i	$-0.210099\pi$
$152$	−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	0.565702	−	0.824610i	$-0.308605\pi$
$157$	−3.63877	−	3.85687i	−0.290406	−	0.307812i	−0.856107	+	0.516798i	$0.827124\pi$
$158$	−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	0.958739	+	0.284286i	$0.0917566\pi$
$167$	15.3368	+	16.2561i	1.18680	+	1.25793i	0.228060	+	0.973647i	$0.426762\pi$
$168$		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	$-0.0502328\pi$
$173$	1.00106	+	3.34376i	0.0761089	+	0.254221i	−0.911465	+	0.411378i	$0.865048\pi$
$174$		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	$-0.579035\pi$
$179$	−14.1428	−	5.14757i	−1.05709	−	0.384748i	−0.811332	+	0.584585i	$0.801257\pi$
$180$		0			0
$181$	−2.01428	+	0.733137i	−0.149720	+	0.0544936i	−0.415793	−	0.909459i	$-0.636496\pi$
$181$	−2.01428	+	0.733137i	−0.149720	+	0.0544936i	0.266073	+	0.963953i	$0.414274\pi$
$182$	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	$-0.919742\pi$
$191$	−18.6097	+	9.34613i	−1.34655	+	0.676262i	−0.378168	+	0.925737i	$0.623446\pi$
$192$		0			0
$193$	8.41707	−	11.3061i	0.605874	−	0.813830i	−0.388310	−	0.921529i	$-0.626941\pi$
$193$	8.41707	−	11.3061i	0.605874	−	0.813830i	0.994184	+	0.107699i	$0.0343484\pi$
$194$	−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	$-0.256035\pi$
$197$	1.46772	+	1.23157i	0.104571	+	0.0877455i	−0.589003	+	0.808131i	$0.700479\pi$
$198$		0			0
$199$	12.3341	−	10.3495i	0.874339	−	0.733658i	−0.0906679	−	0.995881i	$-0.528900\pi$
$199$	12.3341	−	10.3495i	0.874339	−	0.733658i	0.965007	+	0.262223i	$0.0844557\pi$
$200$	−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	−0.0993336	−	0.995054i	$-0.531671\pi$
$211$	3.75461	−	0.889860i	0.258478	−	0.0612605i	0.357812	+	0.933794i	$0.383523\pi$
$212$	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	−0.873919	−	0.486072i	$-0.838429\pi$
$223$	1.18505	−	2.74725i	0.0793567	−	0.183970i	0.953275	+	0.302103i	$0.0976885\pi$
$224$	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	−0.108549	+	0.994091i	$0.534620\pi$
$227$	−16.4925	+	17.4810i	−1.09465	+	1.16026i	−0.986098	+	0.166167i	$0.946861\pi$
$228$		0			0
$229$	−4.22971	−	2.12424i	−0.279507	−	0.140374i	0.303523	−	0.952824i	$-0.401837\pi$
$229$	−4.22971	−	2.12424i	−0.279507	−	0.140374i	−0.583031	+	0.812450i	$0.698133\pi$
$230$	−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	−0.984751	−	0.173968i	$-0.944341\pi$
$233$	−1.81475	−	10.2920i	−0.118888	−	0.674250i	0.865863	−	0.500282i	$-0.166770\pi$
$234$		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	−0.991543	−	0.129782i	$-0.958572\pi$
$239$	−6.26895	−	14.5331i	−0.405504	−	0.940065i	0.586038	−	0.810283i	$-0.300687\pi$
$240$		0			0
$241$	−14.7387	−	9.69379i	−0.949402	−	0.624432i	−0.0225049	−	0.999747i	$-0.507164\pi$
$241$	−14.7387	−	9.69379i	−0.949402	−	0.624432i	−0.926897	+	0.375315i	$0.877535\pi$
$242$	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	0.633936	+	0.773386i	$0.281438\pi$
$251$	−3.58499	+	20.3315i	−0.226282	+	1.28331i	−0.860218	+	0.509926i	$0.829673\pi$
$252$		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	$-0.278864\pi$
$257$	6.51246	+	3.27068i	0.406236	+	0.204019i	−0.233934	+	0.972252i	$0.575160\pi$
$258$		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	$-0.974704\pi$
$263$	−4.13582	+	9.58791i	−0.255026	+	0.591216i	0.741818	+	0.670601i	$0.233964\pi$
$264$		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	0.294585	+	0.955625i	$0.404819\pi$
$269$	−11.1578	+	19.3259i	−0.680304	+	1.17832i	−0.974888	+	0.222695i	$0.928515\pi$
$270$		0			0
$271$	11.6312	+	20.1458i	0.706544	+	1.22377i	0.966132	+	0.258050i	$0.0830800\pi$
$271$	11.6312	+	20.1458i	0.706544	+	1.22377i	−0.259588	+	0.965720i	$0.583587\pi$
$272$	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	0.932151	−	0.362070i	$-0.117930\pi$
$277$	5.29170	+	7.10799i	0.317948	+	0.427078i	−0.614203	+	0.789148i	$0.710522\pi$
$278$	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	$-0.204528\pi$
$281$	20.9045	+	4.95445i	1.24706	+	0.295558i	0.446483	+	0.894792i	$0.352676\pi$
$282$		0			0
$283$	0.511009	−	0.336096i	0.0303763	−	0.0199788i	−0.534230	−	0.845339i	$-0.679398\pi$
$283$	0.511009	−	0.336096i	0.0303763	−	0.0199788i	0.564606	+	0.825360i	$0.309028\pi$
$284$	−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	0.197569	−	0.980289i	$-0.436695\pi$
$293$	18.4868	−	24.8321i	1.08001	−	1.45071i	0.882443	−	0.470419i	$-0.155897\pi$
$294$		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	−0.349882	−	0.936794i	$-0.613778\pi$
$307$	−21.3773	−	7.78069i	−1.22007	−	0.444068i	−0.870184	+	0.492726i	$0.836000\pi$
$308$	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	0.545299	+	0.838242i	$0.316416\pi$
$311$	1.78117	+	30.5816i	0.101001	+	1.73412i	−0.444298	+	0.895879i	$0.646547\pi$
$312$		0			0
$313$	6.54199	+	21.8518i	0.369775	+	1.23513i	0.917250	+	0.398312i	$0.130404\pi$
$313$	6.54199	+	21.8518i	0.369775	+	1.23513i	−0.547475	+	0.836822i	$0.684411\pi$
$314$	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	$-0.464706\pi$
$317$	7.96795	−	0.931320i	0.447525	−	0.0523081i	0.336871	+	0.941551i	$0.390631\pi$
$318$		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	−0.602399	−	0.798195i	$-0.705788\pi$
$331$	−18.2750	+	2.13604i	−1.00448	+	0.117407i	−0.402085	+	0.915602i	$0.631714\pi$
$332$	−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	−0.728022	−	0.685553i	$-0.759560\pi$
$337$	−1.55141	−	26.6366i	−0.0845105	−	1.45099i	0.643512	−	0.765436i	$-0.277477\pi$
$338$	−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	$-0.691822\pi$
$347$	−24.3715	−	2.84862i	−1.30833	−	0.152922i	−0.741522	+	0.670929i	$0.765896\pi$
$348$		0			0
$349$	−0.975561	+	16.7497i	−0.0522206	+	0.896592i	0.865882	+	0.500249i	$0.166758\pi$
$349$	−0.975561	+	16.7497i	−0.0522206	+	0.896592i	−0.918102	+	0.396344i	$0.870279\pi$
$350$	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	$-0.472739\pi$
$353$	17.5821	−	8.83007i	0.935802	−	0.469977i	0.850263	+	0.526357i	$0.176443\pi$
$354$		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	−0.945285	−	0.326245i	$-0.894216\pi$
$359$	−27.1083	−	22.7466i	−1.43072	−	1.20052i	−0.485436	−	0.874272i	$-0.661339\pi$
$360$		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	0.695828	−	0.718208i	$-0.255037\pi$
$367$	19.0674	+	4.51906i	0.995312	+	0.235893i	0.299484	+	0.954101i	$0.403186\pi$
$368$	−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	0.690994	−	0.722860i	$-0.257173\pi$
$373$	31.5367	−	7.47433i	1.63291	−	0.387006i	0.941914	+	0.335854i	$0.109025\pi$
$374$	−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	−0.618731	−	0.785603i	$-0.712353\pi$
$379$	7.22233	−	12.5094i	0.370986	−	0.642567i	0.989718	+	0.143036i	$0.0456863\pi$
$380$	−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	−0.634428	−	0.772982i	$-0.718764\pi$
$383$	6.27015	−	20.9437i	0.320390	−	1.07018i	0.954817	−	0.297193i	$-0.0960506\pi$
$384$		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	$-0.601526\pi$
$389$	12.8716	−	13.6431i	0.652617	−	0.691734i	0.966190	+	0.257830i	$0.0830076\pi$
$390$		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	0.778759	+	0.627323i	$0.215850\pi$
$397$	−3.33925	+	18.9379i	−0.167592	+	0.950463i	−0.946351	+	0.323140i	$0.895262\pi$
$398$	−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	$-0.165595\pi$
$401$	−1.78850	−	4.14622i	−0.0893137	−	0.207052i	−0.957018	+	0.290028i	$0.906335\pi$
$402$		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	0.777428	+	0.628972i	$0.216524\pi$
$409$	14.1854	+	32.8854i	0.701422	+	1.62608i	−0.0760060	+	0.997107i	$0.524217\pi$
$410$	−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	$-0.143396\pi$
$419$	22.2824	+	11.1906i	1.08857	+	0.546698i	0.188332	+	0.982105i	$0.439692\pi$
$420$		0			0
$421$	24.7669	−	26.2513i	1.20706	−	1.27941i	0.257340	−	0.966321i	$-0.417154\pi$
$421$	24.7669	−	26.2513i	1.20706	−	1.27941i	0.949723	−	0.313092i	$-0.101365\pi$
$422$	−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	−0.372587	−	0.927997i	$-0.621529\pi$
$431$	12.8170	−	22.1998i	0.617375	−	1.06933i	0.989963	−	0.141329i	$-0.0451374\pi$
$432$		0			0
$433$	−2.49590	−	4.32302i	−0.119945	−	0.207751i	0.799801	−	0.600266i	$-0.204939\pi$
$433$	−2.49590	−	4.32302i	−0.119945	−	0.207751i	−0.919746	+	0.392515i	$0.871605\pi$
$434$	−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	0.847486	−	0.530818i	$-0.178115\pi$
$439$	2.00946	+	2.69917i	0.0959061	+	0.128824i	−0.751580	+	0.659642i	$0.770708\pi$
$440$	−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	$-0.528932\pi$
$443$	−13.0248	−	3.08693i	−0.618825	−	0.146664i	−0.528059	+	0.849208i	$0.677080\pi$
$444$		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	−0.187906	+	0.982187i	$0.560170\pi$
$449$	−25.1690	+	21.1193i	−1.18780	+	0.996683i	−0.999895	+	0.0144961i	$0.995386\pi$
$450$		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	−0.832783	−	0.553600i	$-0.813254\pi$
$457$	−18.9412	+	9.51261i	−0.886031	+	0.444981i	−0.0532479	+	0.998581i	$0.516957\pi$
$458$	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	0.898398	+	0.439182i	$0.144732\pi$
$461$	−0.964285	+	16.5561i	−0.0449112	+	0.771096i	−0.943309	+	0.331914i	$0.892305\pi$
$462$		0			0
$463$	−3.39720	−	0.397076i	−0.157881	−	0.0184537i	0.0367850	−	0.999323i	$-0.488288\pi$
$463$	−3.39720	−	0.397076i	−0.157881	−	0.0184537i	−0.194666	+	0.980870i	$0.562362\pi$
$464$	−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	$-0.540981\pi$
$467$	8.87582	−	3.23054i	0.410724	−	0.149491i	0.539115	+	0.842232i	$0.318759\pi$
$468$		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	$-0.674091\pi$
$479$	−18.1464	+	2.12101i	−0.829130	+	0.0969114i	−0.309068	+	0.951040i	$0.600017\pi$
$480$		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	$-0.256452\pi$
$491$	−1.50047	−	1.59041i	−0.0677154	−	0.0717741i	−0.760346	+	0.649519i	$0.774970\pi$
$492$		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	0.997390	−	0.0721995i	$-0.0230018\pi$
$499$	−0.0365869	−	0.628173i	−0.00163785	−	0.0281209i	−0.999028	+	0.0440786i	$0.985965\pi$
$500$	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	$-0.344637\pi$
$503$	5.84089	+	2.12591i	0.260432	+	0.0947897i	−0.208504	+	0.978021i	$0.566859\pi$
$504$		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	$-0.599100\pi$
$509$	−18.5886	−	2.17270i	−0.823927	−	0.0963032i	−0.517600	+	0.855623i	$0.673174\pi$
$510$		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	$-0.377253\pi$
$521$	−10.7516	−	9.02171i	−0.471038	−	0.395248i	−0.847173	+	0.531317i	$0.821697\pi$
$522$		0			0
$523$	−15.7777	+	13.2390i	−0.689910	+	0.578903i	−0.918883	−	0.394530i	$-0.870908\pi$
$523$	−15.7777	+	13.2390i	−0.689910	+	0.578903i	0.228973	+	0.973433i	$0.426463\pi$
$524$	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	0.0727213	+	0.997352i	$0.476832\pi$
$541$	−19.2442	+	33.3319i	−0.827372	+	1.43305i	−0.900093	+	0.435698i	$0.856502\pi$
$542$	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	−0.687328	−	0.726347i	$-0.741217\pi$
$547$	7.31275	−	16.9529i	0.312671	−	0.724852i	0.999999	+	0.00149506i	$0.000475892\pi$
$548$	−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	$-0.00691477\pi$
$557$	1.24763	+	7.07568i	0.0528639	+	0.299806i	−0.946900	+	0.321528i	$0.895804\pi$
$558$		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	−0.955749	−	0.294183i	$-0.904952\pi$
$563$	−12.1926	−	28.2655i	−0.513855	−	1.19125i	0.441894	−	0.897067i	$-0.354307\pi$
$564$		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	$-0.0964896\pi$
$569$	25.2451	+	16.6040i	1.05833	+	0.696075i	0.103925	+	0.994585i	$0.466860\pi$
$570$		0			0
$571$	−3.12787	−	7.25122i	−0.130897	−	0.303454i	0.840145	−	0.542362i	$-0.182470\pi$
$571$	−3.12787	−	7.25122i	−0.130897	−	0.303454i	−0.971042	+	0.238908i	$0.923211\pi$
$572$	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	−0.998996	−	0.0448050i	$-0.985733\pi$
$577$	−1.81528	−	10.2950i	−0.0755710	−	0.428585i	0.923425	−	0.383780i	$-0.125378\pi$
$578$	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	$-0.970934\pi$
$587$	−5.96314	+	13.8241i	−0.246125	+	0.570582i	0.749709	+	0.661768i	$0.230194\pi$
$588$		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	$-0.705638\pi$
$593$	9.50914	−	16.4703i	0.390494	−	0.676355i	0.992515	+	0.122125i	$0.0389710\pi$
$594$		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	$-0.876527\pi$
$599$	−38.7477	+	9.18337i	−1.58319	+	0.375222i	−0.657482	+	0.753470i	$0.728379\pi$
$600$		0			0
$601$	3.33430	+	4.47874i	0.136009	+	0.182691i	0.864909	−	0.501928i	$-0.167376\pi$
$601$	3.33430	+	4.47874i	0.136009	+	0.182691i	−0.728901	+	0.684620i	$0.759968\pi$
$602$	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	−0.765313	−	0.643658i	$-0.777416\pi$
$607$	−11.7624	+	7.73624i	−0.477420	+	0.314004i	0.287892	+	0.957663i	$0.407045\pi$
$608$	−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	0.321258	−	0.946992i	$-0.395894\pi$
$613$	−13.7550	−	11.5418i	−0.555561	−	0.466171i	−0.876819	+	0.480821i	$0.840339\pi$
$614$	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	−0.170217	−	0.985407i	$-0.554447\pi$
$617$	20.4332	−	27.4466i	0.822611	−	1.10496i	0.992828	−	0.119552i	$-0.0381458\pi$
$618$		0			0
$619$	−30.9588	+	15.5481i	−1.24434	+	0.624931i	−0.944329	−	0.329004i	$-0.893287\pi$
$619$	−30.9588	+	15.5481i	−1.24434	+	0.624931i	−0.300012	+	0.953935i	$0.596991\pi$
$620$	−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	0.982154	−	0.188080i	$-0.0602263\pi$
$631$	40.5340	+	14.7532i	1.61363	+	0.587314i	0.631478	+	0.775394i	$0.282449\pi$
$632$	−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	$-0.567298\pi$
$641$	−4.77410	+	0.558012i	−0.188566	+	0.0220402i	0.0212859	+	0.999773i	$0.493224\pi$
$642$		0			0
$643$	−5.69244	−	6.03363i	−0.224488	−	0.237943i	0.605334	−	0.795971i	$-0.293040\pi$
$643$	−5.69244	−	6.03363i	−0.224488	−	0.237943i	−0.829822	+	0.558028i	$0.811558\pi$
$644$	−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	0.567155	−	0.823611i	$-0.308044\pi$
$653$	−7.36051	−	7.80169i	−0.288039	−	0.305304i	−0.855195	+	0.518307i	$0.826562\pi$
$654$		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	−0.998905	−	0.0467759i	$-0.985105\pi$
$659$	−4.87841	−	16.2950i	−0.190036	−	0.634764i	0.808870	−	0.587988i	$-0.200080\pi$
$660$		0			0
$661$	1.81584	+	31.1767i	0.0706279	+	1.21263i	0.828409	+	0.560124i	$0.189247\pi$
$661$	1.81584	+	31.1767i	0.0706279	+	1.21263i	−0.757781	+	0.652509i	$0.773716\pi$
$662$	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	−0.976728	−	0.214481i	$-0.931194\pi$
$673$	0.474625	−	8.14899i	0.0182954	−	0.314121i	0.995024	−	0.0996395i	$-0.0317690\pi$
$674$	−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	$-0.681546\pi$
$677$	−4.87031	+	2.44596i	−0.187181	+	0.0940060i	0.352740	+	0.935721i	$0.385250\pi$
$678$		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	$-0.296690\pi$
$683$	−2.37757	−	1.99502i	−0.0909753	−	0.0763374i	−0.687141	+	0.726524i	$0.741135\pi$
$684$		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	0.671760	−	0.740769i	$-0.265539\pi$
$691$	24.6994	+	5.85387i	0.939610	+	0.222692i	0.267850	+	0.963461i	$0.413687\pi$
$692$	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	$-0.160972\pi$
$701$	0.473675	+	0.820430i	0.0178905	+	0.0309872i	−0.856942	+	0.515414i	$0.827638\pi$
$702$		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	−0.490686	−	0.871337i	$-0.663254\pi$
$709$	12.7765	−	29.6192i	0.479831	−	1.11237i	0.970516	−	0.241036i	$-0.0774871\pi$
$710$	−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	−0.951673	−	0.307114i	$-0.900637\pi$
$719$	−4.35548	−	24.7012i	−0.162432	−	0.921198i	0.789241	−	0.614084i	$-0.210474\pi$
$720$		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	0.676973	−	0.736008i	$-0.263292\pi$
$727$	7.26093	+	4.77559i	0.269293	+	0.177117i	−0.407680	+	0.913125i	$0.633662\pi$
$728$	−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	0.969803	−	0.243888i	$-0.0784229\pi$
$733$	3.43532	+	7.96396i	0.126886	+	0.294156i	−0.842917	+	0.538043i	$0.819164\pi$
$734$	−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	0.978533	−	0.206089i	$-0.0660736\pi$
$739$	−0.311908	−	1.76892i	−0.0114737	−	0.0650707i	−0.990007	+	0.141018i	$0.954962\pi$
$740$	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	$-0.211066\pi$
$743$	20.8516	+	10.4721i	0.764972	+	0.384183i	−0.0231267	+	0.999733i	$0.507362\pi$
$744$		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	0.794388	+	0.607411i	$0.207792\pi$
$751$	−5.56559	+	18.5904i	−0.203091	+	0.678373i	−0.997479	+	0.0709615i	$0.977393\pi$
$752$	−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	0.668617	−	0.743607i	$-0.266886\pi$
$757$	−8.52025	−	14.7575i	−0.309674	−	0.536371i	−0.978291	+	0.207236i	$0.933553\pi$
$758$	−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	$-0.290697\pi$
$761$	41.7260	−	9.88923i	1.51256	−	0.358484i	0.901389	+	0.433011i	$0.142549\pi$
$762$		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	−0.901023	−	0.433771i	$-0.857183\pi$
$769$	−23.8376	+	15.6782i	−0.859605	+	0.565371i	0.0414182	+	0.999142i	$0.486812\pi$
$770$	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	$-0.457111\pi$
$773$	31.5157	−	26.4448i	1.13354	−	0.951155i	0.999208	+	0.0397813i	$0.0126661\pi$
$774$		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
$783$		0			0
$784$	−13.6647	+	23.6679i	−0.488023	+	0.845281i
$785$	1.03910	−	17.8406i	0.0370869	−	0.636758i
$786$		0			0
$787$	20.7254	+	2.42245i	0.738779	+	0.0863509i	0.477155	−	0.878819i	$-0.341668\pi$
$787$	20.7254	+	2.42245i	0.738779	+	0.0863509i	0.261624	+	0.965170i	$0.415742\pi$
$788$	1.09058	−	3.64281i	0.0388505	−	0.129770i
$789$		0			0
$790$	0.929177	−	2.15408i	0.0330586	−	0.0766386i
$791$	−48.2584	+	17.5646i	−1.71587	+	0.624526i
$792$		0			0
$793$	6.34161	+	2.30816i	0.225197	+	0.0819650i
$794$	1.63474	−	1.73273i	0.0580148	−	0.0614921i
$795$		0			0
$796$	−28.5559	−	14.3413i	−1.01214	−	0.508315i
$797$	−2.33298	−	40.0557i	−0.0826383	−	1.41884i	−0.743700	−	0.668513i	$-0.766931\pi$
$797$	−2.33298	−	40.0557i	−0.0826383	−	1.41884i	0.661062	−	0.750331i	$-0.270106\pi$
$798$		0			0
$799$	−4.50031	−	15.0321i	−0.159210	−	0.531797i
$800$	1.62467	+	9.21395i	0.0574407	+	0.325762i
$801$		0			0
$802$	−0.0971339	+	0.550874i	−0.00342992	+	0.0194520i
$803$	73.1601	−	8.55119i	2.58176	−	0.301765i
$804$		0			0
$805$	9.23865	+	9.79240i	0.325620	+	0.345137i
$806$	−0.423356	−	0.981450i	−0.0149121	−	0.0345701i
$807$		0			0
$808$	−2.25809	−	1.48517i	−0.0794392	−	0.0522480i
$809$	−25.7049			−0.903736			−0.451868	−	0.892085i	$-0.649242\pi$
$809$	−25.7049			−0.903736			−0.451868	+	0.892085i	$0.649242\pi$
$810$		0			0
$811$	37.0961			1.30262			0.651310	−	0.758812i	$-0.274220\pi$
$811$	37.0961			1.30262			0.651310	+	0.758812i	$0.274220\pi$
$812$	−11.1848	−	7.35637i	−0.392510	−	0.258158i
$813$		0			0
$814$	0.721282	+	1.67212i	0.0252809	+	0.0586078i
$815$	−11.2555	−	11.9301i	−0.394263	−	0.417895i
$816$		0			0
$817$	10.0898	−	1.17933i	0.352998	−	0.0412595i
$818$	0.770410	−	4.36921i	0.0269367	−	0.152766i
$819$		0			0
$820$	−1.17097	−	6.64091i	−0.0408921	−	0.231911i
$821$	−6.82772	−	22.8062i	−0.238289	−	0.795941i	−0.990559	−	0.137086i	$-0.956226\pi$
$821$	−6.82772	−	22.8062i	−0.238289	−	0.795941i	0.752270	−	0.658855i	$-0.228959\pi$
$822$		0			0
$823$	−0.654427	−	11.2361i	−0.0228119	−	0.391665i	−0.990318	−	0.138817i	$-0.955670\pi$
$823$	−0.654427	−	11.2361i	−0.0228119	−	0.391665i	0.967506	−	0.252848i	$-0.0813671\pi$
$824$	1.03427	+	0.519428i	0.0360304	+	0.0180951i
$825$		0			0
$826$	−3.38652	+	3.58950i	−0.117832	+	0.124895i
$827$	−20.1174	−	7.32212i	−0.699549	−	0.254615i	−0.0323307	−	0.999477i	$-0.510293\pi$
$827$	−20.1174	−	7.32212i	−0.699549	−	0.254615i	−0.667218	+	0.744862i	$0.732515\pi$
$828$		0			0
$829$	−0.656956	+	0.239112i	−0.0228170	+	0.00830471i	−0.353403	−	0.935471i	$-0.614976\pi$
$829$	−0.656956	+	0.239112i	−0.0228170	+	0.00830471i	0.330586	+	0.943776i	$0.392753\pi$
$830$	−1.99389	+	4.62235i	−0.0692089	+	0.160444i
$831$		0			0
$832$	−2.78336	+	9.29707i	−0.0964956	+	0.322318i
$833$	−11.4392	−	1.33705i	−0.396344	−	0.0463260i
$834$		0			0
$835$	−4.37962	+	75.1952i	−0.151563	+	2.60224i
$836$	−19.9885	+	34.6211i	−0.691317	+	1.19740i
$837$		0			0
$838$	−1.54442	−	2.67501i	−0.0533511	−	0.0924068i
$839$	−33.1138	+	16.6304i	−1.14322	+	0.574145i	−0.916587	−	0.399836i	$-0.869067\pi$
$839$	−33.1138	+	16.6304i	−1.14322	+	0.574145i	−0.226630	+	0.973981i	$0.572771\pi$
$840$		0			0
$841$	−15.3759	+	20.6534i	−0.530202	+	0.712185i
$842$	−4.35031	+	1.03104i	−0.149922	+	0.0355320i
$843$		0			0
$844$	−4.57306	−	6.14268i	−0.157411	−	0.211440i
$845$	29.3909	+	24.6619i	1.01108	+	0.848395i
$846$		0			0
$847$	−28.2267	+	23.6850i	−0.969882	+	0.813828i
$848$	−10.9505	−	2.59531i	−0.376041	−	0.0891232i
$849$		0			0
$850$	−1.08392	+	0.712903i	−0.0371780	+	0.0244524i
$851$	−2.87226	+	1.88911i	−0.0984598	+	0.0647580i
$852$		0			0
$853$	−14.7524	−	3.49638i	−0.505113	−	0.119714i	−0.0298439	−	0.999555i	$-0.509501\pi$
$853$	−14.7524	−	3.49638i	−0.505113	−	0.119714i	−0.475269	+	0.879841i	$0.657649\pi$
$854$	−1.88445	+	1.58124i	−0.0644845	+	0.0541089i
$855$		0			0
$856$	−4.44962	−	3.73368i	−0.152085	−	0.127614i
$857$	−3.65333	−	4.90727i	−0.124795	−	0.167629i	0.735335	−	0.677704i	$-0.237025\pi$
$857$	−3.65333	−	4.90727i	−0.124795	−	0.167629i	−0.860130	+	0.510075i	$0.829618\pi$
$858$		0			0
$859$	−5.71378	+	1.35419i	−0.194952	+	0.0462044i	−0.326932	−	0.945048i	$-0.606015\pi$
$859$	−5.71378	+	1.35419i	−0.194952	+	0.0462044i	0.131980	+	0.991252i	$0.457867\pi$
$860$	−9.19819	+	12.3553i	−0.313656	+	0.421313i
$861$		0			0
$862$	−2.83772	+	1.42516i	−0.0966532	+	0.0485411i
$863$	−0.872485	−	1.51119i	−0.0296997	−	0.0514414i	0.850794	−	0.525500i	$-0.176122\pi$
$863$	−0.872485	−	1.51119i	−0.0296997	−	0.0514414i	−0.880493	+	0.474059i	$0.842788\pi$
$864$		0			0
$865$	−5.88182	+	10.1876i	−0.199988	+	0.346389i
$866$	−0.0359551	+	0.617326i	−0.00122181	+	0.0209776i
$867$		0			0
$868$	−50.0486	−	5.84985i	−1.69876	−	0.198557i
$869$	−7.35863	+	24.5795i	−0.249624	+	0.833804i
$870$		0			0
$871$	1.53120	−	3.54972i	0.0518828	−	0.120278i
$872$	0.196474	−	0.0715107i	0.00665345	−	0.00242166i
$873$		0			0
$874$	0.548351	+	0.199583i	0.0185482	+	0.00675100i
$875$	−11.7561	+	12.4608i	−0.397430	+	0.421251i
$876$		0			0
$877$	42.1682	+	21.1777i	1.42392	+	0.715120i	0.983201	−	0.182525i	$-0.0584272\pi$
$877$	42.1682	+	21.1777i	1.42392	+	0.715120i	0.440719	+	0.897645i	$0.354723\pi$
$878$	−0.0242378	−	0.416147i	−0.000817986	−	0.0140443i
$879$		0			0
$880$	−17.2497	−	57.6179i	−0.581486	−	1.94230i
$881$	3.06509	+	17.3830i	0.103266	+	0.585648i	0.991899	+	0.127030i	$0.0405443\pi$
$881$	3.06509	+	17.3830i	0.103266	+	0.585648i	−0.888633	+	0.458618i	$0.848345\pi$
$882$		0			0
$883$	1.28101	−	7.26495i	0.0431093	−	0.244485i	−0.955637	−	0.294548i	$-0.904831\pi$
$883$	1.28101	−	7.26495i	0.0431093	−	0.244485i	0.998746	+	0.0500627i	$0.0159421\pi$
$884$	−4.12718	+	0.482398i	−0.138812	+	0.0162248i
$885$		0			0
$886$	1.13791	+	1.20611i	0.0382288	+	0.0405201i
$887$	−1.16804	−	2.70782i	−0.0392190	−	0.0909199i	0.897481	−	0.441054i	$-0.145395\pi$
$887$	−1.16804	−	2.70782i	−0.0392190	−	0.0909199i	−0.936700	+	0.350134i	$0.886136\pi$
$888$		0			0
$889$	11.3186	+	7.44433i	0.379612	+	0.249675i
$890$	−4.08296			−0.136861
$891$		0			0
$892$	−5.93798			−0.198818
$893$	−35.1141	−	23.0949i	−1.17505	−	0.772842i
$894$		0			0
$895$	−20.0909	−	46.5760i	−0.671566	−	1.55687i
$896$	−9.98162	−	10.5799i	−0.333463	−	0.353450i
$897$		0			0
$898$	4.04259	−	0.472511i	0.134903	−	0.0157679i
$899$	2.12530	−	12.0532i	0.0708828	−	0.401996i
$900$		0			0
$901$	−0.823536	−	4.67050i	−0.0274360	−	0.155597i
$902$	−0.163553	−	0.546305i	−0.00544572	−	0.0181900i
$903$		0			0
$904$	−0.394029	−	6.76522i	−0.0131052	−	0.225008i
$905$	−6.45594	−	3.24229i	−0.214603	−	0.107777i
$906$		0			0
$907$	−4.94770	+	5.24426i	−0.164286	+	0.174133i	−0.804287	−	0.594241i	$-0.797452\pi$
$907$	−4.94770	+	5.24426i	−0.164286	+	0.174133i	0.640001	+	0.768374i	$0.278934\pi$
$908$	44.8209	+	16.3135i	1.48743	+	0.541382i
$909$		0			0
$910$	1.86565	−	0.679040i	0.0618456	−	0.0225099i
$911$	−5.67990	+	13.1675i	−0.188183	+	0.436258i	−0.986022	−	0.166612i	$-0.946717\pi$
$911$	−5.67990	+	13.1675i	−0.188183	+	0.436258i	0.797839	+	0.602870i	$0.205976\pi$
$912$		0			0
$913$	15.7906	−	52.7443i	0.522593	−	1.74558i
$914$	2.60792	+	0.304822i	0.0862623	+	0.0100826i
$915$		0			0
$916$	−0.546195	+	9.37781i	−0.0180468	+	0.309851i
$917$	−11.6893	+	20.2465i	−0.386015	+	0.668598i
$918$		0			0
$919$	23.7632	+	41.1591i	0.783875	+	1.35771i	0.929669	+	0.368397i	$0.120093\pi$
$919$	23.7632	+	41.1591i	0.783875	+	1.35771i	−0.145793	+	0.989315i	$0.546573\pi$
$920$	−1.58752	+	0.797285i	−0.0523391	+	0.0262857i
$921$		0			0
$922$	1.22681	−	1.64789i	0.0404028	−	0.0542704i
$923$	2.46967	−	0.585323i	0.0812903	−	0.0192661i
$924$		0			0
$925$	−12.2247	−	16.4207i	−0.401947	−	0.539909i
$926$	0.324575	+	0.272351i	0.0106662	+	0.00895000i
$927$		0			0
$928$	2.03246	−	1.70543i	0.0667186	−	0.0559836i
$929$	49.6586	+	11.7693i	1.62925	+	0.386138i	0.940750	−	0.339102i	$-0.110123\pi$
$929$	49.6586	+	11.7693i	1.62925	+	0.386138i	0.688496	+	0.725240i	$0.258271\pi$
$930$		0			0
$931$	−25.7730	+	16.9512i	−0.844676	+	0.555552i
$932$	−17.3290	+	11.3974i	−0.567629	+	0.373335i
$933$		0			0
$934$	−1.13854	−	0.269839i	−0.0372542	−	0.00882941i
$935$	19.4161	−	16.2921i	0.634976	−	0.532808i
$936$		0			0
$937$	−22.5978	−	18.9618i	−0.738237	−	0.619454i	0.194127	−	0.980976i	$-0.437813\pi$
$937$	−22.5978	−	18.9618i	−0.738237	−	0.619454i	−0.932364	+	0.361522i	$0.882257\pi$
$938$	0.841504	+	1.13034i	0.0274761	+	0.0369068i
$939$		0			0
$940$	62.0095	−	14.6965i	2.02253	−	0.479347i
$941$	−35.0824	+	47.1239i	−1.14366	+	1.53620i	−0.340683	+	0.940178i	$0.610658\pi$
$941$	−35.0824	+	47.1239i	−1.14366	+	1.53620i	−0.802972	+	0.596017i	$0.796749\pi$
$942$		0			0
$943$	0.962042	−	0.483156i	0.0313284	−	0.0157337i
$944$	20.8100	+	36.0440i	0.677309	+	1.17313i
$945$		0			0
$946$	−0.651300	+	1.12808i	−0.0211756	+	0.0366772i
$947$	0.685195	−	11.7644i	0.0222659	−	0.382290i	−0.968705	−	0.248214i	$-0.920156\pi$
$947$	0.685195	−	11.7644i	0.0222659	−	0.382290i	0.990971	−	0.134076i	$-0.0428066\pi$
$948$		0			0
$949$	20.3679	+	2.38067i	0.661172	+	0.0772799i
$950$	−0.996605	+	3.32889i	−0.0323341	+	0.108004i
$951$		0			0
$952$	1.20449	−	2.79233i	0.0390379	−	0.0905000i
$953$	33.2006	−	12.0840i	1.07547	−	0.391441i	0.257253	−	0.966344i	$-0.417183\pi$
$953$	33.2006	−	12.0840i	1.07547	−	0.391441i	0.818221	+	0.574904i	$0.194960\pi$
$954$		0			0
$955$	−65.9527	−	24.0048i	−2.13418	−	0.776778i
$956$	−21.5563	+	22.8483i	−0.697180	+	0.738968i
$957$		0			0
$958$	2.02250	+	1.01574i	0.0653441	+	0.0328170i
$959$	−3.56188	−	61.1551i	−0.115019	−	1.97480i
$960$		0			0
$961$	−4.32158	−	14.4351i	−0.139406	−	0.465648i
$962$	0.0880371	+	0.499283i	0.00283843	+	0.0160975i
$963$		0			0
$964$	−6.07958	+	34.4790i	−0.195810	+	1.11049i
$965$	47.1836	−	5.51498i	1.51890	−	0.177533i
$966$		0			0
$967$	39.2923	+	41.6475i	1.26356	+	1.33929i	0.915762	+	0.401721i	$0.131588\pi$
$967$	39.2923	+	41.6475i	1.26356	+	1.33929i	0.347794	+	0.937571i	$0.386931\pi$
$968$	−1.92584	−	4.46459i	−0.0618988	−	0.143497i
$969$		0			0
$970$	−3.27734	−	2.15554i	−0.105229	−	0.0692101i
$971$	−25.0907			−0.805200			−0.402600	−	0.915376i	$-0.631893\pi$
$971$	−25.0907			−0.805200			−0.402600	+	0.915376i	$0.631893\pi$
$972$		0			0
$973$	−73.1022			−2.34355
$974$	−3.23078	−	2.12491i	−0.103521	−	0.0680867i
$975$		0			0
$976$	8.21748	+	19.0503i	0.263035	+	0.609784i
$977$	−20.2855	−	21.5013i	−0.648989	−	0.687889i	0.316422	−	0.948618i	$-0.397518\pi$
$977$	−20.2855	−	21.5013i	−0.648989	−	0.687889i	−0.965412	+	0.260730i	$0.916037\pi$
$978$		0			0
$979$	44.3533	−	5.18415i	1.41754	−	0.165686i
$980$	8.12229	−	46.0638i	0.259457	−	1.47145i
$981$		0			0
$982$	0.0470343	+	0.266745i	0.00150092	+	0.00851216i
$983$	13.9538	+	46.6090i	0.445057	+	1.48659i	0.826890	+	0.562364i	$0.190108\pi$
$983$	13.9538	+	46.6090i	0.445057	+	1.48659i	−0.381833	+	0.924231i	$0.624707\pi$
$984$		0			0
$985$	0.375464	+	6.44647i	0.0119633	+	0.205402i
$986$	0.328766	+	0.165113i	0.0104701	+	0.00525826i
$987$		0			0
$988$	−7.63766	+	8.09545i	−0.242986	+	0.257550i
$989$	−2.31077	−	0.841053i	−0.0734783	−	0.0267439i
$990$		0			0
$991$	20.7603	−	7.55612i	0.659472	−	0.240028i	0.00946345	−	0.999955i	$-0.496988\pi$
$991$	20.7603	−	7.55612i	0.659472	−	0.240028i	0.650008	+	0.759927i	$0.274765\pi$
$992$	3.95549	−	9.16985i	0.125587	−	0.291143i
$993$		0			0
$994$	−0.265343	+	0.886307i	−0.00841616	+	0.0281119i
$995$	53.8980	+	6.29978i	1.70868	+	0.199716i
$996$		0			0
$997$	−0.378868	+	6.50491i	−0.0119989	+	0.206013i	0.986980	+	0.160841i	$0.0514206\pi$
$997$	−0.378868	+	6.50491i	−0.0119989	+	0.206013i	−0.998979	+	0.0451718i	$0.985616\pi$
$998$	−0.0389742	+	0.0675054i	−0.00123371	+	0.00213684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.703.4		144
3.2	odd	2		729.2.g.a.703.5		144
9.2	odd	6		243.2.g.a.235.5		144
9.4	even	3		729.2.g.c.460.5		144
9.5	odd	6		729.2.g.b.460.4		144
9.7	even	3		81.2.g.a.79.4	yes	144
81.13	even	27		81.2.g.a.40.4	✓	144
81.14	odd	54		729.2.g.a.28.5		144
81.38	odd	54		6561.2.a.d.1.36		72
81.40	even	27		729.2.g.c.271.5		144
81.41	odd	54		729.2.g.b.271.4		144
81.43	even	27		6561.2.a.c.1.37		72
81.67	even	27	inner	729.2.g.d.28.4		144
81.68	odd	54		243.2.g.a.91.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.4	✓	144	81.13	even	27
81.2.g.a.79.4	yes	144	9.7	even	3
243.2.g.a.91.5		144	81.68	odd	54
243.2.g.a.235.5		144	9.2	odd	6
729.2.g.a.28.5		144	81.14	odd	54
729.2.g.a.703.5		144	3.2	odd	2
729.2.g.b.271.4		144	81.41	odd	54
729.2.g.b.460.4		144	9.5	odd	6
729.2.g.c.271.5		144	81.40	even	27
729.2.g.c.460.5		144	9.4	even	3
729.2.g.d.28.4		144	81.67	even	27	inner
729.2.g.d.703.4		144	1.1	even	1	trivial
6561.2.a.c.1.37		72	81.43	even	27
6561.2.a.d.1.36		72	81.38	odd	54

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

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