LMFDB - Embedded newform 729.2.g.a.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	729.109
Dual form			729.2.g.a.622.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31250 - 1.39117i) q^{2} +(-0.0964037 + 1.65519i) q^{4} +(2.46793 - 0.288460i) q^{5} +(-4.06877 - 2.04341i) q^{7} +(-0.501084 + 0.420459i) q^{8} +O(q^{10})$	\(q+(-1.31250 - 1.39117i) q^{2} +(-0.0964037 + 1.65519i) q^{4} +(2.46793 - 0.288460i) q^{5} +(-4.06877 - 2.04341i) q^{7} +(-0.501084 + 0.420459i) q^{8} +(-3.64045 - 3.05470i) q^{10} +(-0.125874 - 0.291810i) q^{11} +(-3.31064 - 0.784636i) q^{13} +(2.49752 + 8.34231i) q^{14} +(4.53616 + 0.530202i) q^{16} +(-0.885565 + 5.02229i) q^{17} +(-0.216164 - 1.22593i) q^{19} +(0.239538 + 4.11270i) q^{20} +(-0.240746 + 0.558112i) q^{22} +(1.70487 - 0.856218i) q^{23} +(1.14226 - 0.270720i) q^{25} +(3.25365 + 5.63548i) q^{26} +(3.77448 - 6.53759i) q^{28} +(-0.993943 + 3.32000i) q^{29} +(-5.67009 - 3.72928i) q^{31} +(-4.43488 - 5.95708i) q^{32} +(8.14914 - 5.35978i) q^{34} +(-10.6309 - 3.86933i) q^{35} +(-8.02231 + 2.91988i) q^{37} +(-1.42176 + 1.90975i) q^{38} +(-1.11536 + 1.18221i) q^{40} +(-4.35826 + 4.61948i) q^{41} +(-3.63719 + 4.88559i) q^{43} +(0.495135 - 0.180214i) q^{44} +(-3.42878 - 1.24797i) q^{46} +(3.40689 - 2.24075i) q^{47} +(8.19925 + 11.0135i) q^{49} +(-1.87583 - 1.23375i) q^{50} +(1.61788 - 5.40409i) q^{52} +(3.88136 - 6.72271i) q^{53} +(-0.394825 - 0.683857i) q^{55} +(2.89797 - 0.686831i) q^{56} +(5.92322 - 2.97475i) q^{58} +(-1.57205 + 3.64441i) q^{59} +(-0.142985 - 2.45496i) q^{61} +(2.25394 + 12.7827i) q^{62} +(-0.880398 + 4.99299i) q^{64} +(-8.39677 - 0.981441i) q^{65} +(0.988137 + 3.30061i) q^{67} +(-8.22746 - 1.94994i) q^{68} +(8.57015 + 19.8678i) q^{70} +(2.16099 + 1.81328i) q^{71} +(-3.24023 + 2.71887i) q^{73} +(14.5913 + 7.32803i) q^{74} +(2.04998 - 0.239609i) q^{76} +(-0.0841338 + 1.44452i) q^{77} +(4.97152 + 5.26950i) q^{79} +11.3479 q^{80} +12.1467 q^{82} +(-8.29076 - 8.78769i) q^{83} +(-0.736786 + 12.6501i) q^{85} +(11.5705 - 1.35239i) q^{86} +(0.185768 + 0.0932961i) q^{88} +(-2.86182 + 2.40135i) q^{89} +(11.8669 + 9.95751i) q^{91} +(1.25285 + 2.90442i) q^{92} +(-7.58878 - 1.79857i) q^{94} +(-0.887111 - 2.96316i) q^{95} +(-14.5265 - 1.69791i) q^{97} +(4.56012 - 25.8617i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31250	−	1.39117i	−0.928076	−	0.983703i	0.0718301	−	0.997417i	$-0.477116\pi$
$2$	−1.31250	−	1.39117i	−0.928076	−	0.983703i	−0.999906	+	0.0137139i	$0.995635\pi$
$3$		0			0
$3$		0			0
$4$	−0.0964037	+	1.65519i	−0.0482019	+	0.827594i
$5$	2.46793	−	0.288460i	1.10369	−	0.129003i	0.455321	−	0.890327i	$-0.349524\pi$
$5$	2.46793	−	0.288460i	1.10369	−	0.129003i	0.648372	+	0.761324i	$0.275450\pi$
$6$		0			0
$7$	−4.06877	−	2.04341i	−1.53785	−	0.772338i	−0.540246	−	0.841507i	$-0.681669\pi$
$7$	−4.06877	−	2.04341i	−1.53785	−	0.772338i	−0.997605	+	0.0691692i	$0.977965\pi$
$8$	−0.501084	+	0.420459i	−0.177160	+	0.148655i
$9$		0			0
$10$	−3.64045	−	3.05470i	−1.15121	−	0.965981i
$11$	−0.125874	−	0.291810i	−0.0379526	−	0.0879840i	0.898185	−	0.439617i	$-0.144886\pi$
$11$	−0.125874	−	0.291810i	−0.0379526	−	0.0879840i	−0.936138	+	0.351633i	$0.885627\pi$
$12$		0			0
$13$	−3.31064	−	0.784636i	−0.918206	−	0.217619i	−0.255770	−	0.966738i	$-0.582329\pi$
$13$	−3.31064	−	0.784636i	−0.918206	−	0.217619i	−0.662436	+	0.749119i	$0.730477\pi$
$14$	2.49752	+	8.34231i	0.667492	+	2.22958i
$15$		0			0
$16$	4.53616	+	0.530202i	1.13404	+	0.132550i
$17$	−0.885565	+	5.02229i	−0.214781	+	1.21808i	0.666505	+	0.745501i	$0.267790\pi$
$17$	−0.885565	+	5.02229i	−0.214781	+	1.21808i	−0.881286	+	0.472584i	$0.843321\pi$
$18$		0			0
$19$	−0.216164	−	1.22593i	−0.0495915	−	0.281248i	0.949920	−	0.312493i	$-0.101164\pi$
$19$	−0.216164	−	1.22593i	−0.0495915	−	0.281248i	−0.999512	+	0.0312449i	$0.990053\pi$
$20$	0.239538	+	4.11270i	0.0535622	+	0.919628i
$21$		0			0
$22$	−0.240746	+	0.558112i	−0.0513272	+	0.118990i
$23$	1.70487	−	0.856218i	0.355490	−	0.178534i	−0.262087	−	0.965044i	$-0.584411\pi$
$23$	1.70487	−	0.856218i	0.355490	−	0.178534i	0.617577	+	0.786510i	$0.288114\pi$
$24$		0			0
$25$	1.14226	−	0.270720i	0.228452	−	0.0541440i
$26$	3.25365	+	5.63548i	0.638092	+	1.10521i
$27$		0			0
$28$	3.77448	−	6.53759i	0.713309	−	1.23549i
$29$	−0.993943	+	3.32000i	−0.184571	+	0.616509i	0.814756	+	0.579805i	$0.196871\pi$
$29$	−0.993943	+	3.32000i	−0.184571	+	0.616509i	−0.999326	+	0.0367041i	$0.988314\pi$
$30$		0			0
$31$	−5.67009	−	3.72928i	−1.01838	−	0.669798i	−0.0735253	−	0.997293i	$-0.523425\pi$
$31$	−5.67009	−	3.72928i	−1.01838	−	0.669798i	−0.944853	+	0.327496i	$0.893795\pi$
$32$	−4.43488	−	5.95708i	−0.783984	−	1.05307i
$33$		0			0
$34$	8.14914	−	5.35978i	1.39757	−	0.919194i
$35$	−10.6309	−	3.86933i	−1.79695	−	0.654036i
$36$		0			0
$37$	−8.02231	+	2.91988i	−1.31886	+	0.480026i	−0.903093	−	0.429445i	$-0.858709\pi$
$37$	−8.02231	+	2.91988i	−1.31886	+	0.480026i	−0.415767	+	0.909471i	$0.636487\pi$
$38$	−1.42176	+	1.90975i	−0.230639	+	0.309802i
$39$		0			0
$40$	−1.11536	+	1.18221i	−0.176353	+	0.186923i
$41$	−4.35826	+	4.61948i	−0.680646	+	0.721442i	−0.971950	−	0.235188i	$-0.924429\pi$
$41$	−4.35826	+	4.61948i	−0.680646	+	0.721442i	0.291304	+	0.956630i	$0.405911\pi$
$42$		0			0
$43$	−3.63719	+	4.88559i	−0.554666	+	0.745046i	−0.987705	−	0.156329i	$-0.950034\pi$
$43$	−3.63719	+	4.88559i	−0.554666	+	0.745046i	0.433039	+	0.901375i	$0.357441\pi$
$44$	0.495135	−	0.180214i	0.0746444	−	0.0271683i
$45$		0			0
$46$	−3.42878	−	1.24797i	−0.505546	−	0.184004i
$47$	3.40689	−	2.24075i	0.496946	−	0.326846i	−0.276173	−	0.961108i	$-0.589066\pi$
$47$	3.40689	−	2.24075i	0.496946	−	0.326846i	0.773119	+	0.634262i	$0.218696\pi$
$48$		0			0
$49$	8.19925	+	11.0135i	1.17132	+	1.57336i
$50$	−1.87583	−	1.23375i	−0.265282	−	0.174479i
$51$		0			0
$52$	1.61788	−	5.40409i	0.224359	−	0.749412i
$53$	3.88136	−	6.72271i	0.533146	−	0.923435i	−0.466105	−	0.884729i	$-0.654343\pi$
$53$	3.88136	−	6.72271i	0.533146	−	0.923435i	0.999251	−	0.0387058i	$-0.0123235\pi$
$54$		0			0
$55$	−0.394825	−	0.683857i	−0.0532382	−	0.0922113i
$56$	2.89797	−	0.686831i	0.387257	−	0.0917817i
$57$		0			0
$58$	5.92322	−	2.97475i	0.777757	−	0.390604i
$59$	−1.57205	+	3.64441i	−0.204663	+	0.474462i	−0.989373	−	0.145401i	$-0.953553\pi$
$59$	−1.57205	+	3.64441i	−0.204663	+	0.474462i	0.784710	+	0.619863i	$0.212812\pi$
$60$		0			0
$61$	−0.142985	−	2.45496i	−0.0183074	−	0.314325i	−0.995013	−	0.0997428i	$-0.968198\pi$
$61$	−0.142985	−	2.45496i	−0.0183074	−	0.314325i	0.976706	−	0.214582i	$-0.0688390\pi$
$62$	2.25394	+	12.7827i	0.286250	+	1.62340i
$63$		0			0
$64$	−0.880398	+	4.99299i	−0.110050	+	0.624123i
$65$	−8.39677	−	0.981441i	−1.04149	−	0.121733i
$66$		0			0
$67$	0.988137	+	3.30061i	0.120720	+	0.403233i	0.996893	−	0.0787630i	$-0.0250970\pi$
$67$	0.988137	+	3.30061i	0.120720	+	0.403233i	−0.876173	+	0.481996i	$0.839912\pi$
$68$	−8.22746	−	1.94994i	−0.997726	−	0.236466i
$69$		0			0
$70$	8.57015	+	19.8678i	1.02433	+	2.37466i
$71$	2.16099	+	1.81328i	0.256462	+	0.215197i	0.761949	−	0.647637i	$-0.224243\pi$
$71$	2.16099	+	1.81328i	0.256462	+	0.215197i	−0.505487	+	0.862834i	$0.668687\pi$
$72$		0			0
$73$	−3.24023	+	2.71887i	−0.379240	+	0.318220i	−0.812404	−	0.583095i	$-0.801842\pi$
$73$	−3.24023	+	2.71887i	−0.379240	+	0.318220i	0.433164	+	0.901315i	$0.357397\pi$
$74$	14.5913	+	7.32803i	1.69621	+	0.851866i
$75$		0			0
$76$	2.04998	−	0.239609i	0.235149	−	0.0274850i
$77$	−0.0841338	+	1.44452i	−0.00958793	+	0.164618i
$78$		0			0
$79$	4.97152	+	5.26950i	0.559339	+	0.592865i	0.943899	−	0.330235i	$-0.107128\pi$
$79$	4.97152	+	5.26950i	0.559339	+	0.592865i	−0.384559	+	0.923100i	$0.625647\pi$
$80$	11.3479			1.26873
$81$		0			0
$82$	12.1467			1.34138
$83$	−8.29076	−	8.78769i	−0.910029	−	0.964575i	0.0894773	−	0.995989i	$-0.471480\pi$
$83$	−8.29076	−	8.78769i	−0.910029	−	0.964575i	−0.999506	+	0.0314144i	$0.989999\pi$
$84$		0			0
$85$	−0.736786	+	12.6501i	−0.0799157	+	1.37210i
$86$	11.5705	−	1.35239i	1.24768	−	0.145832i
$87$		0			0
$88$	0.185768	+	0.0932961i	0.0198029	+	0.00994540i
$89$	−2.86182	+	2.40135i	−0.303352	+	0.254543i	−0.781738	−	0.623607i	$-0.785666\pi$
$89$	−2.86182	+	2.40135i	−0.303352	+	0.254543i	0.478386	+	0.878150i	$0.341222\pi$
$90$		0			0
$91$	11.8669	+	9.95751i	1.24399	+	1.04383i
$92$	1.25285	+	2.90442i	0.130618	+	0.302807i
$93$		0			0
$94$	−7.58878	−	1.79857i	−0.782723	−	0.185509i
$95$	−0.887111	−	2.96316i	−0.0910157	−	0.304013i
$96$		0			0
$97$	−14.5265	−	1.69791i	−1.47495	−	0.172396i	−0.659707	−	0.751523i	$-0.729320\pi$
$97$	−14.5265	−	1.69791i	−1.47495	−	0.172396i	−0.815238	+	0.579126i	$0.803394\pi$
$98$	4.56012	−	25.8617i	0.460642	−	2.61243i
$99$		0			0
$100$	0.337975	+	1.91675i	0.0337975	+	0.191675i
$101$	1.03108	+	17.7029i	0.102596	+	1.76150i	0.521293	+	0.853378i	$0.325450\pi$
$101$	1.03108	+	17.7029i	0.102596	+	1.76150i	−0.418697	+	0.908126i	$0.637513\pi$
$102$		0			0
$103$	5.64552	−	13.0878i	0.556269	−	1.28958i	−0.375600	−	0.926782i	$-0.622563\pi$
$103$	5.64552	−	13.0878i	0.556269	−	1.28958i	0.931869	−	0.362795i	$-0.118178\pi$
$104$	1.98882	−	0.998820i	0.195019	−	0.0979424i
$105$		0			0
$106$	−14.4467	+	3.42393i	−1.40319	+	0.332561i
$107$	−1.70493	−	2.95303i	−0.164822	−	0.285480i	0.771770	−	0.635902i	$-0.219372\pi$
$107$	−1.70493	−	2.95303i	−0.164822	−	0.285480i	−0.936592	+	0.350422i	$0.886038\pi$
$108$		0			0
$109$	−0.0867949	+	0.150333i	−0.00831345	+	0.0143993i	−0.870152	−	0.492783i	$-0.835980\pi$
$109$	−0.0867949	+	0.150333i	−0.00831345	+	0.0143993i	0.861839	+	0.507182i	$0.169313\pi$
$110$	−0.433152	+	1.44683i	−0.0412994	+	0.137950i
$111$		0			0
$112$	−17.3732	−	11.4265i	−1.64161	−	1.07971i
$113$	1.19330	+	1.60288i	0.112256	+	0.150786i	0.854700	−	0.519122i	$-0.173741\pi$
$113$	1.19330	+	1.60288i	0.112256	+	0.150786i	−0.742444	+	0.669908i	$0.766333\pi$
$114$		0			0
$115$	3.96052	−	2.60488i	0.369321	−	0.242906i
$116$	−5.39940	−	1.96522i	−0.501322	−	0.182466i
$117$		0			0
$118$	7.13329	−	2.59630i	0.656672	−	0.239009i
$119$	13.8658	−	18.6250i	1.27107	−	1.70735i
$120$		0			0
$121$	7.47935	−	7.92765i	0.679941	−	0.720695i
$122$	−3.22759	+	3.42104i	−0.292212	+	0.309727i
$123$		0			0
$124$	6.71927	−	9.02555i	0.603408	−	0.810518i
$125$	−8.93351	+	3.25153i	−0.799037	+	0.290826i
$126$		0			0
$127$	2.99061	+	1.08849i	0.265374	+	0.0965883i	0.471280	−	0.881983i	$-0.343792\pi$
$127$	2.99061	+	1.08849i	0.265374	+	0.0965883i	−0.205906	+	0.978572i	$0.566014\pi$
$128$	−4.30814	+	2.83351i	−0.380789	+	0.250449i
$129$		0			0
$130$	9.65539	+	12.9694i	0.846834	+	1.13750i
$131$	−9.47526	−	6.23198i	−0.827858	−	0.544491i	0.0633998	−	0.997988i	$-0.479806\pi$
$131$	−9.47526	−	6.23198i	−0.827858	−	0.544491i	−0.891257	+	0.453498i	$0.850176\pi$
$132$		0			0
$133$	−1.62556	+	5.42974i	−0.140954	+	0.470818i
$134$	3.29477	−	5.70670i	0.284624	−	0.492984i
$135$		0			0
$136$	−1.66793	−	2.88893i	−0.143024	−	0.247724i
$137$	−9.44692	+	2.23896i	−0.807105	+	0.191287i	−0.613400	−	0.789772i	$-0.710199\pi$
$137$	−9.44692	+	2.23896i	−0.807105	+	0.191287i	−0.193705	+	0.981060i	$0.562050\pi$
$138$		0			0
$139$	6.34545	−	3.18681i	0.538214	−	0.270301i	−0.158859	−	0.987301i	$-0.550781\pi$
$139$	6.34545	−	3.18681i	0.538214	−	0.270301i	0.697073	+	0.717000i	$0.254485\pi$
$140$	7.42933	−	17.2231i	0.627893	−	1.45562i
$141$		0			0
$142$	−0.313712	−	5.38623i	−0.0263261	−	0.452002i
$143$	0.187760	+	1.06484i	0.0157013	+	0.0890466i
$144$		0			0
$145$	−1.49530	+	8.48025i	−0.124178	+	0.704246i
$146$	8.03520	+	0.939180i	0.664998	+	0.0777271i
$147$		0			0
$148$	−4.05958	−	13.5599i	−0.333695	−	1.11462i
$149$	20.6828	+	4.90190i	1.69440	+	0.401580i	0.960632	−	0.277824i	$-0.0896131\pi$
$149$	20.6828	+	4.90190i	1.69440	+	0.401580i	0.733765	+	0.679403i	$0.237761\pi$
$150$		0			0
$151$	−7.98827	−	18.5189i	−0.650076	−	1.50705i	−0.849751	−	0.527184i	$-0.823248\pi$
$151$	−7.98827	−	18.5189i	−0.650076	−	1.50705i	0.199674	−	0.979862i	$-0.436012\pi$
$152$	0.623770	+	0.523405i	0.0505944	+	0.0424538i
$153$		0			0
$154$	2.11999	−	1.77889i	0.170834	−	0.143347i
$155$	−15.0691	−	7.56801i	−1.21038	−	0.607877i
$156$		0			0
$157$	8.02804	−	0.938344i	0.640708	−	0.0748880i	0.210465	−	0.977601i	$-0.432502\pi$
$157$	8.02804	−	0.938344i	0.640708	−	0.0748880i	0.430242	+	0.902713i	$0.358428\pi$
$158$	0.805646	−	13.8324i	0.0640938	−	1.10045i
$159$		0			0
$160$	−12.6634	−	13.4224i	−1.00113	−	1.06113i
$161$	−8.68634			−0.684579
$162$		0			0
$163$	−9.17644			−0.718754			−0.359377	−	0.933192i	$-0.617011\pi$
$163$	−9.17644			−0.718754			−0.359377	+	0.933192i	$0.617011\pi$
$164$	−7.22596	−	7.65907i	−0.564253	−	0.598073i
$165$		0			0
$166$	−1.34354	+	23.0676i	−0.104279	+	1.79040i
$167$	−16.2411	+	1.89831i	−1.25677	+	0.146896i	−0.718292	−	0.695742i	$-0.755076\pi$
$167$	−16.2411	+	1.89831i	−1.25677	+	0.146896i	−0.538481	+	0.842638i	$0.681002\pi$
$168$		0			0
$169$	−1.27255	−	0.639099i	−0.0978886	−	0.0491615i
$170$	18.5655	−	15.5783i	1.42391	−	1.19480i
$171$		0			0
$172$	−7.73593	−	6.49122i	−0.589859	−	0.494951i
$173$	−4.67529	−	10.8385i	−0.355456	−	0.824039i	−0.998313	−	0.0580532i	$-0.981511\pi$
$173$	−4.67529	−	10.8385i	−0.355456	−	0.824039i	0.642858	−	0.765985i	$-0.277749\pi$
$174$		0			0
$175$	−5.20078	−	1.23261i	−0.393142	−	0.0931763i
$176$	−0.416269	−	1.39044i	−0.0313775	−	0.104808i
$177$		0			0
$178$	7.09680	+	0.829498i	0.531928	+	0.0621735i
$179$	1.09845	−	6.22965i	0.0821024	−	0.465626i	−0.915842	−	0.401539i	$-0.868475\pi$
$179$	1.09845	−	6.22965i	0.0821024	−	0.465626i	0.997944	−	0.0640868i	$-0.0204134\pi$
$180$		0			0
$181$	−2.97786	−	16.8883i	−0.221342	−	1.25530i	−0.869555	−	0.493836i	$-0.835594\pi$
$181$	−2.97786	−	16.8883i	−0.221342	−	1.25530i	0.648213	−	0.761459i	$-0.275517\pi$
$182$	−1.72272	−	29.5780i	−0.127697	−	2.19247i
$183$		0			0
$184$	−0.494278	+	1.14587i	−0.0364387	+	0.0844744i
$185$	−18.9563	+	9.52019i	−1.39369	+	0.699939i
$186$		0			0
$187$	1.57702	−	0.373761i	0.115323	−	0.0273321i
$188$	3.38042	+	5.85506i	0.246542	+	0.427024i
$189$		0			0
$190$	−2.95791	+	5.12325i	−0.214590	+	0.371680i
$191$	2.20578	−	7.36781i	0.159604	−	0.533116i	−0.840356	−	0.542035i	$-0.817654\pi$
$191$	2.20578	−	7.36781i	0.159604	−	0.533116i	0.999960	+	0.00891931i	$0.00283914\pi$
$192$		0			0
$193$	−7.94542	−	5.22578i	−0.571924	−	0.376160i	0.230358	−	0.973106i	$-0.426010\pi$
$193$	−7.94542	−	5.22578i	−0.571924	−	0.376160i	−0.802282	+	0.596946i	$0.796381\pi$
$194$	16.7040	+	22.4373i	1.19927	+	1.61090i
$195$		0			0
$196$	−19.0199	+	12.5096i	−1.35856	+	0.893540i
$197$	−8.26958	−	3.00988i	−0.589183	−	0.214445i	0.0301870	−	0.999544i	$-0.490390\pi$
$197$	−8.26958	−	3.00988i	−0.589183	−	0.214445i	−0.619370	+	0.785099i	$0.712612\pi$
$198$		0			0
$199$	−1.90131	+	0.692020i	−0.134780	+	0.0490560i	−0.408530	−	0.912745i	$-0.633958\pi$
$199$	−1.90131	+	0.692020i	−0.134780	+	0.0490560i	0.273749	+	0.961801i	$0.411736\pi$
$200$	−0.458540	+	0.615926i	−0.0324237	+	0.0435526i
$201$		0			0
$202$	23.2744	−	24.6694i	1.63758	−	1.73573i
$203$	10.8283	−	11.4773i	0.759995	−	0.805548i
$204$		0			0
$205$	−9.42335	+	12.6578i	−0.658155	+	0.884056i
$206$	−25.6170	+	9.32383i	−1.78482	+	0.649622i
$207$		0			0
$208$	−14.6016	−	5.31454i	−1.01244	−	0.368497i
$209$	−0.330529	+	0.217392i	−0.0228631	+	0.0150373i
$210$		0			0
$211$	−15.4367	−	20.7351i	−1.06271	−	1.42746i	−0.897399	−	0.441219i	$-0.854546\pi$
$211$	−15.4367	−	20.7351i	−1.06271	−	1.42746i	−0.165306	−	0.986242i	$-0.552861\pi$
$212$	10.7532	+	7.07247i	0.738531	+	0.485739i
$213$		0			0
$214$	−1.87043	+	6.24768i	−0.127860	+	0.427083i
$215$	−7.56704	+	13.1065i	−0.516068	+	0.893856i
$216$		0			0
$217$	15.4498	+	26.7599i	1.04880	+	1.81658i
$218$	0.323057	−	0.0765658i	0.0218802	−	0.00518569i
$219$		0			0
$220$	1.16997	−	0.587583i	0.0788797	−	0.0396149i
$221$	6.87246	−	15.9321i	0.462291	−	1.07171i
$222$		0			0
$223$	0.500206	+	8.58821i	0.0334963	+	0.575109i	0.972746	+	0.231874i	$0.0744857\pi$
$223$	0.500206	+	8.58821i	0.0334963	+	0.575109i	−0.939250	+	0.343235i	$0.888477\pi$
$224$	5.87174	+	33.3003i	0.392322	+	2.22497i
$225$		0			0
$226$	0.663669	−	3.76385i	0.0441466	−	0.250368i
$227$	18.3416	+	2.14382i	1.21737	+	0.142290i	0.700425	−	0.713726i	$-0.252994\pi$
$227$	18.3416	+	2.14382i	1.21737	+	0.142290i	0.516948	+	0.856017i	$0.327068\pi$
$228$		0			0
$229$	0.0335266	+	0.111987i	0.00221550	+	0.00740029i	0.959090	−	0.283101i	$-0.0913631\pi$
$229$	0.0335266	+	0.111987i	0.00221550	+	0.00740029i	−0.956875	+	0.290501i	$0.906178\pi$
$230$	−8.82199	−	2.09085i	−0.581705	−	0.137867i
$231$		0			0
$232$	−0.897876	−	2.08151i	−0.0589485	−	0.136658i
$233$	8.71132	+	7.30967i	0.570698	+	0.478872i	0.881877	−	0.471479i	$-0.156280\pi$
$233$	8.71132	+	7.30967i	0.570698	+	0.478872i	−0.311180	+	0.950351i	$0.600724\pi$
$234$		0			0
$235$	7.76161	−	6.51276i	0.506311	−	0.424846i
$236$	−5.88063	−	2.95337i	−0.382797	−	0.192248i
$237$		0			0
$238$	−44.1092	+	5.15563i	−2.85918	+	0.334190i
$239$	0.349285	−	5.99699i	0.0225933	−	0.387913i	−0.967989	−	0.250993i	$-0.919243\pi$
$239$	0.349285	−	5.99699i	0.0225933	−	0.387913i	0.990582	−	0.136919i	$-0.0437202\pi$
$240$		0			0
$241$	−12.9006	−	13.6738i	−0.831000	−	0.880808i	0.163393	−	0.986561i	$-0.447756\pi$
$241$	−12.9006	−	13.6738i	−0.831000	−	0.880808i	−0.994392	+	0.105753i	$0.966275\pi$
$242$	−20.8453			−1.33999
$243$		0			0
$244$	4.07720			0.261016
$245$	23.4122	+	24.8154i	1.49575	+	1.58540i
$246$		0			0
$247$	−0.246266	+	4.22822i	−0.0156695	+	0.269035i
$248$	4.40920	−	0.515361i	0.279984	−	0.0327255i
$249$		0			0
$250$	16.2486	+	8.16036i	1.02765	+	0.516107i
$251$	13.5256	−	11.3493i	0.853727	−	0.716362i	−0.106880	−	0.994272i	$-0.534086\pi$
$251$	13.5256	−	11.3493i	0.853727	−	0.716362i	0.960607	+	0.277910i	$0.0896417\pi$
$252$		0			0
$253$	−0.464453	−	0.389722i	−0.0291999	−	0.0245016i
$254$	−2.41090	−	5.58909i	−0.151273	−	0.350691i
$255$		0			0
$256$	19.4630	+	4.61282i	1.21644	+	0.288301i
$257$	−3.80309	−	12.7032i	−0.237230	−	0.792404i	−0.990835	−	0.135076i	$-0.956872\pi$
$257$	−3.80309	−	12.7032i	−0.237230	−	0.792404i	0.753605	−	0.657327i	$-0.228313\pi$
$258$		0			0
$259$	38.6075	+	4.51257i	2.39895	+	0.280397i
$260$	2.43395	−	13.8036i	0.150947	−	0.856064i
$261$		0			0
$262$	3.76654	+	21.3611i	0.232698	+	1.31969i
$263$	0.134508	+	2.30941i	0.00829411	+	0.142404i	0.999913	+	0.0132054i	$0.00420353\pi$
$263$	0.134508	+	2.30941i	0.00829411	+	0.142404i	−0.991619	+	0.129199i	$0.958759\pi$
$264$		0			0
$265$	7.63970	−	17.7108i	0.469303	−	1.08797i
$266$	9.68721	−	4.86510i	0.593961	−	0.298298i
$267$		0			0
$268$	−5.55838	+	1.31736i	−0.339532	+	0.0804707i
$269$	9.15670	+	15.8599i	0.558294	+	0.966993i	0.997639	+	0.0686749i	$0.0218771\pi$
$269$	9.15670	+	15.8599i	0.558294	+	0.966993i	−0.439345	+	0.898318i	$0.644790\pi$
$270$		0			0
$271$	−4.57582	+	7.92556i	−0.277961	+	0.481443i	−0.970878	−	0.239574i	$-0.922992\pi$
$271$	−4.57582	+	7.92556i	−0.277961	+	0.481443i	0.692917	+	0.721018i	$0.256325\pi$
$272$	−6.67990	+	22.3124i	−0.405028	+	1.35289i
$273$		0			0
$274$	15.5138	+	10.2036i	0.937225	+	0.616422i
$275$	−0.222780	−	0.299245i	−0.0134341	−	0.0180452i
$276$		0			0
$277$	13.9017	−	9.14326i	0.835270	−	0.549365i	−0.0582954	−	0.998299i	$-0.518567\pi$
$277$	13.9017	−	9.14326i	0.835270	−	0.549365i	0.893565	+	0.448934i	$0.148196\pi$
$278$	−12.7618	−	4.64490i	−0.765400	−	0.278583i
$279$		0			0
$280$	6.95387	−	2.53100i	0.415573	−	0.151256i
$281$	−4.10706	+	5.51674i	−0.245007	+	0.329101i	−0.907567	−	0.419908i	$-0.862062\pi$
$281$	−4.10706	+	5.51674i	−0.245007	+	0.329101i	0.662560	+	0.749009i	$0.269470\pi$
$282$		0			0
$283$	−15.3917	+	16.3142i	−0.914940	+	0.969780i	−0.999645	−	0.0266265i	$-0.991524\pi$
$283$	−15.3917	+	16.3142i	−0.914940	+	0.969780i	0.0847057	+	0.996406i	$0.473005\pi$
$284$	−3.20965	+	3.40203i	−0.190458	+	0.201874i
$285$		0			0
$286$	1.23494	−	1.65881i	0.0730234	−	0.0980874i
$287$	27.1723	−	9.88990i	1.60393	−	0.583782i
$288$		0			0
$289$	−8.46441	−	3.08079i	−0.497906	−	0.181223i
$290$	13.7600	−	9.05010i	0.808016	−	0.531440i
$291$		0			0
$292$	−4.18788	−	5.62529i	−0.245077	−	0.329195i
$293$	−10.5713	−	6.95288i	−0.617584	−	0.406191i	0.201808	−	0.979425i	$-0.435318\pi$
$293$	−10.5713	−	6.95288i	−0.617584	−	0.406191i	−0.819392	+	0.573234i	$0.805689\pi$
$294$		0			0
$295$	−2.82844	+	9.44763i	−0.164678	+	0.550062i
$296$	2.79216	−	4.83616i	0.162291	−	0.281096i
$297$		0			0
$298$	−20.3267	−	35.2069i	−1.17749	−	2.03948i
$299$	−6.31603	+	1.49693i	−0.365265	+	0.0865695i
$300$		0			0
$301$	24.7822	−	12.4461i	1.42842	−	0.717380i
$302$	−15.2783	+	35.4190i	−0.879166	+	2.03814i
$303$		0			0
$304$	−0.330568	−	5.67563i	−0.0189594	−	0.325520i
$305$	−1.06103	−	6.01743i	−0.0607547	−	0.344557i
$306$		0			0
$307$	0.146594	−	0.831376i	0.00836656	−	0.0474491i	−0.980339	−	0.197322i	$-0.936775\pi$
$307$	0.146594	−	0.831376i	0.00836656	−	0.0474491i	0.988705	+	0.149873i	$0.0478865\pi$
$308$	−2.38284	−	0.278514i	−0.135775	−	0.0158698i
$309$		0			0
$310$	9.24986	+	30.8967i	0.525357	+	1.75481i
$311$	5.28171	+	1.25179i	0.299498	+	0.0709824i	0.377618	−	0.925962i	$-0.376743\pi$
$311$	5.28171	+	1.25179i	0.299498	+	0.0709824i	−0.0781194	+	0.996944i	$0.524892\pi$
$312$		0			0
$313$	−8.47295	−	19.6425i	−0.478919	−	1.11026i	−0.970863	−	0.239633i	$-0.922973\pi$
$313$	−8.47295	−	19.6425i	−0.478919	−	1.11026i	0.491944	−	0.870627i	$-0.336286\pi$
$314$	−11.8422	−	9.93677i	−0.668293	−	0.560764i
$315$		0			0
$316$	−9.20128	+	7.72079i	−0.517613	+	0.434329i
$317$	−3.56497	−	1.79040i	−0.200229	−	0.100559i	0.345860	−	0.938286i	$-0.387587\pi$
$317$	−3.56497	−	1.79040i	−0.200229	−	0.100559i	−0.546088	+	0.837728i	$0.683884\pi$
$318$		0			0
$319$	1.09392	−	0.127861i	0.0612478	−	0.00715884i
$320$	−0.732487	+	12.5763i	−0.0409472	+	0.703037i
$321$		0			0
$322$	11.4008	+	12.0841i	0.635342	+	0.673423i
$323$	6.34840			0.353235
$324$		0			0
$325$	−3.99402			−0.221548
$326$	12.0441	+	12.7660i	0.667058	+	0.707041i
$327$		0			0
$328$	0.241548	−	4.14722i	0.0133373	−	0.228992i
$329$	−18.4406	+	2.15540i	−1.01666	+	0.118831i
$330$		0			0
$331$	6.81748	+	3.42387i	0.374722	+	0.188193i	0.626185	−	0.779674i	$-0.284615\pi$
$331$	6.81748	+	3.42387i	0.374722	+	0.188193i	−0.251463	+	0.967867i	$0.580912\pi$
$332$	15.3445	−	12.8756i	0.842141	−	0.706640i
$333$		0			0
$334$	23.9572	+	20.1025i	1.31088	+	1.09996i
$335$	3.39075	+	7.86064i	0.185256	+	0.429472i
$336$		0			0
$337$	−5.20770	−	1.23425i	−0.283682	−	0.0672338i	0.0863117	−	0.996268i	$-0.472492\pi$
$337$	−5.20770	−	1.23425i	−0.283682	−	0.0672338i	−0.369993	+	0.929034i	$0.620640\pi$
$338$	0.781127	+	2.60915i	0.0424877	+	0.141919i
$339$		0			0
$340$	−20.8673	−	2.43904i	−1.13169	−	0.132275i
$341$	−0.374520	+	2.12401i	−0.0202814	+	0.115021i
$342$		0			0
$343$	−5.32131	−	30.1786i	−0.287323	−	1.62949i
$344$	−0.231656	−	3.97738i	−0.0124901	−	0.214446i
$345$		0			0
$346$	−8.94190	+	20.7297i	−0.480720	+	1.11443i
$347$	−11.8237	+	5.93808i	−0.634729	+	0.318773i	−0.736908	−	0.675993i	$-0.763715\pi$
$347$	−11.8237	+	5.93808i	−0.634729	+	0.318773i	0.102179	+	0.994766i	$0.467419\pi$
$348$		0			0
$349$	17.6443	−	4.18177i	0.944478	−	0.223845i	0.270603	−	0.962691i	$-0.412777\pi$
$349$	17.6443	−	4.18177i	0.944478	−	0.223845i	0.673875	+	0.738846i	$0.264629\pi$
$350$	5.11125	+	8.85294i	0.273208	+	0.473210i
$351$		0			0
$352$	−1.18010	+	2.04399i	−0.0628993	+	0.108945i
$353$	−2.04595	+	6.83396i	−0.108895	+	0.363735i	−0.995016	−	0.0997200i	$-0.968205\pi$
$353$	−2.04595	+	6.83396i	−0.108895	+	0.363735i	0.886120	+	0.463455i	$0.153390\pi$
$354$		0			0
$355$	5.85623	+	3.85171i	0.310817	+	0.204427i
$356$	−3.69880	−	4.96834i	−0.196036	−	0.263322i
$357$		0			0
$358$	−10.1082	+	6.64826i	−0.534235	+	0.351372i
$359$	−12.5991	−	4.58570i	−0.664955	−	0.242024i	−0.0125808	−	0.999921i	$-0.504005\pi$
$359$	−12.5991	−	4.58570i	−0.664955	−	0.242024i	−0.652374	+	0.757897i	$0.726227\pi$
$360$		0			0
$361$	16.3980	−	5.96838i	0.863052	−	0.314125i
$362$	−19.5860	+	26.3085i	−1.02942	+	1.38274i
$363$		0			0
$364$	−17.6256	+	18.6820i	−0.923830	+	0.979203i
$365$	−7.21238	+	7.64467i	−0.377513	+	0.400140i
$366$		0			0
$367$	10.9070	−	14.6507i	0.569341	−	0.764758i	−0.420445	−	0.907318i	$-0.638126\pi$
$367$	10.9070	−	14.6507i	0.569341	−	0.764758i	0.989786	+	0.142560i	$0.0455334\pi$
$368$	8.18754	−	2.98002i	0.426805	−	0.155344i
$369$		0			0
$370$	38.1242	+	13.8761i	1.98198	+	0.721383i
$371$	−29.5296	+	19.4219i	−1.53310	+	1.00834i
$372$		0			0
$373$	19.1475	+	25.7195i	0.991418	+	1.33171i	0.942969	+	0.332880i	$0.108021\pi$
$373$	19.1475	+	25.7195i	0.991418	+	1.33171i	0.0484494	+	0.998826i	$0.484572\pi$
$374$	−2.58980	−	1.70334i	−0.133916	−	0.0880777i
$375$		0			0
$376$	−0.764995	+	2.55526i	−0.0394516	+	0.131777i
$377$	5.89558	−	10.2114i	0.303638	−	0.525916i
$378$		0			0
$379$	7.00123	+	12.1265i	0.359629	+	0.622896i	0.987899	−	0.155100i	$-0.0495698\pi$
$379$	7.00123	+	12.1265i	0.359629	+	0.622896i	−0.628270	+	0.777996i	$0.716237\pi$
$380$	4.99010	−	1.18268i	0.255987	−	0.0606700i
$381$		0			0
$382$	−13.1449	+	6.60163i	−0.672553	+	0.337769i
$383$	−2.75853	+	6.39500i	−0.140954	+	0.326769i	−0.974040	−	0.226374i	$-0.927313\pi$
$383$	−2.75853	+	6.39500i	−0.140954	+	0.326769i	0.833086	+	0.553144i	$0.186572\pi$
$384$		0			0
$385$	0.209050	+	3.58925i	0.0106542	+	0.182925i
$386$	3.15841	+	17.9122i	0.160759	+	0.911708i
$387$		0			0
$388$	4.21077	−	23.8804i	0.213769	−	1.21235i
$389$	−7.36338	−	0.860656i	−0.373338	−	0.0436370i	−0.0726449	−	0.997358i	$-0.523144\pi$
$389$	−7.36338	−	0.860656i	−0.373338	−	0.0436370i	−0.300693	+	0.953721i	$0.597218\pi$
$390$		0			0
$391$	2.79040	+	9.32060i	0.141117	+	0.471363i
$392$	−8.73924	−	2.07124i	−0.441399	−	0.104613i
$393$		0			0
$394$	6.66656	+	15.4548i	0.335856	+	0.778603i
$395$	13.7894	+	11.5707i	0.693820	+	0.582184i
$396$		0			0
$397$	8.17232	−	6.85739i	0.410157	−	0.344163i	−0.414247	−	0.910165i	$-0.635955\pi$
$397$	8.17232	−	6.85739i	0.410157	−	0.344163i	0.824404	+	0.566002i	$0.191511\pi$
$398$	3.45818	+	1.73676i	0.173343	+	0.0870561i
$399$		0			0
$400$	5.32500	−	0.622404i	0.266250	−	0.0311202i
$401$	−1.35688	+	23.2967i	−0.0677593	+	1.16338i	0.777449	+	0.628945i	$0.216513\pi$
$401$	−1.35688	+	23.2967i	−0.0677593	+	1.16338i	−0.845209	+	0.534436i	$0.820524\pi$
$402$		0			0
$403$	15.8455	+	16.7952i	0.789320	+	0.836630i
$404$	−29.4010			−1.46275
$405$		0			0
$406$	−30.1789			−1.49775
$407$	1.86186	+	1.97345i	0.0922887	+	0.0978203i
$408$		0			0
$409$	−0.540996	+	9.28854i	−0.0267505	+	0.459289i	0.958161	+	0.286230i	$0.0924022\pi$
$409$	−0.540996	+	9.28854i	−0.0267505	+	0.459289i	−0.984911	+	0.173059i	$0.944635\pi$
$410$	29.9772	−	3.50383i	1.48047	−	0.173042i
$411$		0			0
$412$	21.1185	+	10.6061i	1.04043	+	0.522525i
$413$	13.8433	−	11.6159i	0.681186	−	0.571583i
$414$		0			0
$415$	−22.9959	−	19.2959i	−1.12883	−	0.947197i
$416$	10.0082	+	23.2015i	0.490690	+	1.13755i
$417$		0			0
$418$	0.736247	+	0.174494i	0.0360110	+	0.00853476i
$419$	−0.819783	−	2.73827i	−0.0400490	−	0.133773i	0.935627	−	0.352990i	$-0.114835\pi$
$419$	−0.819783	−	2.73827i	−0.0400490	−	0.133773i	−0.975676	+	0.219217i	$0.929650\pi$
$420$		0			0
$421$	−16.4045	−	1.91741i	−0.799507	−	0.0934490i	−0.293478	−	0.955966i	$-0.594813\pi$
$421$	−16.4045	−	1.91741i	−0.799507	−	0.0934490i	−0.506028	+	0.862517i	$0.668887\pi$
$422$	−8.58531	+	48.6897i	−0.417927	+	2.37018i
$423$		0			0
$424$	0.881740	+	5.00059i	0.0428211	+	0.242850i
$425$	0.348091	+	5.97649i	0.0168849	+	0.289902i
$426$		0			0
$427$	−4.43472	+	10.2808i	−0.214611	+	0.497525i
$428$	5.05218	−	2.53730i	0.244206	−	0.122645i
$429$		0			0
$430$	28.1650	−	6.67523i	1.35824	−	0.321908i
$431$	−11.8861	−	20.5874i	−0.572534	−	0.991658i	−0.996305	−	0.0858887i	$-0.972627\pi$
$431$	−11.8861	−	20.5874i	−0.572534	−	0.991658i	0.423771	−	0.905770i	$-0.360706\pi$
$432$		0			0
$433$	1.46651	−	2.54007i	0.0704761	−	0.122068i	−0.828634	−	0.559791i	$-0.810881\pi$
$433$	1.46651	−	2.54007i	0.0704761	−	0.122068i	0.899110	+	0.437723i	$0.144215\pi$
$434$	16.9496	−	56.6156i	0.813607	−	2.71764i
$435$		0			0
$436$	−0.240462	−	0.158155i	−0.0115161	−	0.00757423i
$437$	−1.41820	−	1.90497i	−0.0678415	−	0.0911270i
$438$		0			0
$439$	−28.0688	+	18.4611i	−1.33965	+	0.881101i	−0.998268	−	0.0588237i	$-0.981265\pi$
$439$	−28.0688	+	18.4611i	−1.33965	+	0.881101i	−0.341381	+	0.939925i	$0.610895\pi$
$440$	0.485375	+	0.176662i	0.0231393	+	0.00842203i
$441$		0			0
$442$	−31.1843	+	11.3502i	−1.48329	+	0.539873i
$443$	−14.4028	+	19.3463i	−0.684298	+	0.919172i	−0.999555	−	0.0298345i	$-0.990502\pi$
$443$	−14.4028	+	19.3463i	−0.684298	+	0.919172i	0.315257	+	0.949006i	$0.397909\pi$
$444$		0			0
$445$	−6.37008	+	6.75189i	−0.301971	+	0.320070i
$446$	11.2911	−	11.9679i	0.534649	−	0.566695i
$447$		0			0
$448$	13.7849	−	18.5163i	0.651274	−	0.874813i
$449$	−26.2610	+	9.55821i	−1.23933	+	0.451080i	−0.876784	−	0.480885i	$-0.840315\pi$
$449$	−26.2610	+	9.55821i	−1.23933	+	0.451080i	−0.362548	+	0.931965i	$0.618093\pi$
$450$		0			0
$451$	1.89660	+	0.690307i	0.0893076	+	0.0325053i
$452$	−2.76811	+	1.82061i	−0.130201	+	0.0856344i
$453$		0			0
$454$	−21.0909	−	28.3299i	−0.989843	−	1.32959i
$455$	32.1590	+	21.1513i	1.50764	+	0.991590i
$456$		0			0
$457$	4.09856	−	13.6901i	0.191722	−	0.640397i	−0.807032	−	0.590507i	$-0.798928\pi$
$457$	4.09856	−	13.6901i	0.191722	−	0.640397i	0.998755	−	0.0498901i	$-0.0158871\pi$
$458$	0.111788	−	0.193623i	0.00522353	−	0.00904742i
$459$		0			0
$460$	3.92975	+	6.80653i	0.183226	+	0.317356i
$461$	−2.39048	+	0.566553i	−0.111336	+	0.0263870i	−0.285906	−	0.958258i	$-0.592295\pi$
$461$	−2.39048	+	0.566553i	−0.111336	+	0.0263870i	0.174570	+	0.984645i	$0.444146\pi$
$462$		0			0
$463$	−34.5822	+	17.3678i	−1.60717	+	0.807152i	−0.607252	+	0.794509i	$0.707728\pi$
$463$	−34.5822	+	17.3678i	−1.60717	+	0.807152i	−0.999920	+	0.0126434i	$0.995975\pi$
$464$	−6.26896	+	14.5331i	−0.291029	+	0.674681i
$465$		0			0
$466$	−1.26463	−	21.7128i	−0.0585827	−	1.00583i
$467$	4.62538	+	26.2318i	0.214037	+	1.21386i	0.882570	+	0.470181i	$0.155811\pi$
$467$	4.62538	+	26.2318i	0.214037	+	1.21386i	−0.668533	+	0.743682i	$0.733078\pi$
$468$		0			0
$469$	2.72400	−	15.4486i	0.125783	−	0.713350i
$470$	−19.2474	−	2.24970i	−0.887818	−	0.103771i
$471$		0			0
$472$	−0.744600	−	2.48714i	−0.0342730	−	0.114480i
$473$	1.88349	+	0.446396i	0.0866031	+	0.0205253i
$474$		0			0
$475$	−0.578799	−	1.34181i	−0.0265571	−	0.0615663i
$476$	29.4911	+	24.7460i	1.35172	+	1.13423i
$477$		0			0
$478$	−8.80124	+	7.38512i	−0.402559	+	0.337787i
$479$	31.7855	+	15.9633i	1.45232	+	0.729381i	0.987734	−	0.156148i	$-0.0499076\pi$
$479$	31.7855	+	15.9633i	1.45232	+	0.729381i	0.464584	+	0.885529i	$0.346204\pi$
$480$		0			0
$481$	28.8500	−	3.37208i	1.31545	−	0.153754i
$482$	−2.09057	+	35.8937i	−0.0952229	+	1.63491i
$483$		0			0
$484$	12.4007	+	13.1440i	0.563669	+	0.597454i
$485$	−36.3403			−1.65013
$486$		0			0
$487$	1.87640			0.0850280			0.0425140	−	0.999096i	$-0.486463\pi$
$487$	1.87640			0.0850280			0.0425140	+	0.999096i	$0.486463\pi$
$488$	1.10386	+	1.17002i	0.0499693	+	0.0529644i
$489$		0			0
$490$	3.79400	−	65.1404i	0.171395	−	2.94274i
$491$	−17.9620	+	2.09945i	−0.810612	+	0.0947469i	−0.511293	−	0.859406i	$-0.670833\pi$
$491$	−17.9620	+	2.09945i	−0.810612	+	0.0947469i	−0.299318	+	0.954153i	$0.596759\pi$
$492$		0			0
$493$	−15.7938	−	7.93195i	−0.711317	−	0.357237i
$494$	6.20538	−	5.20693i	0.279193	−	0.234271i
$495$		0			0
$496$	−23.7432	−	19.9229i	−1.06610	−	0.894565i
$497$	−5.08728	−	11.7936i	−0.228196	−	0.529017i
$498$		0			0
$499$	2.66390	+	0.631357i	0.119253	+	0.0282634i	0.289809	−	0.957085i	$-0.406408\pi$
$499$	2.66390	+	0.631357i	0.119253	+	0.0282634i	−0.170556	+	0.985348i	$0.554556\pi$
$500$	−4.52067	−	15.1001i	−0.202171	−	0.675297i
$501$		0			0
$502$	−33.5411	−	3.92039i	−1.49701	−	0.174975i
$503$	2.34646	−	13.3074i	0.104624	−	0.593350i	−0.886746	−	0.462256i	$-0.847040\pi$
$503$	2.34646	−	13.3074i	0.104624	−	0.593350i	0.991370	−	0.131094i	$-0.0418488\pi$
$504$		0			0
$505$	7.65120	+	43.3921i	0.340474	+	1.93092i
$506$	0.0674248	+	1.15764i	0.00299740	+	0.0514634i
$507$		0			0
$508$	−2.08997	+	4.84509i	−0.0927274	+	0.214966i
$509$	36.8483	−	18.5059i	1.63327	−	0.820260i	0.634389	−	0.773014i	$-0.281252\pi$
$509$	36.8483	−	18.5059i	1.63327	−	0.820260i	0.998883	−	0.0472465i	$-0.0150446\pi$
$510$		0			0
$511$	18.7395	−	4.44135i	0.828988	−	0.196474i
$512$	−13.9715	−	24.1994i	−0.617459	−	1.06947i
$513$		0			0
$514$	−12.6807	+	21.9636i	−0.559322	+	0.968775i
$515$	10.1575	−	33.9283i	0.447591	−	1.49506i
$516$		0			0
$517$	−1.08271	−	0.712111i	−0.0476176	−	0.0313186i
$518$	−44.3945	−	59.6322i	−1.95058	−	2.62009i
$519$		0			0
$520$	4.62014	−	3.03871i	0.202607	−	0.133256i
$521$	11.5074	+	4.18834i	0.504147	+	0.183494i	0.581558	−	0.813505i	$-0.302443\pi$
$521$	11.5074	+	4.18834i	0.504147	+	0.183494i	−0.0774113	+	0.996999i	$0.524665\pi$
$522$		0			0
$523$	4.32620	−	1.57461i	0.189171	−	0.0688527i	−0.245697	−	0.969347i	$-0.579017\pi$
$523$	4.32620	−	1.57461i	0.189171	−	0.0688527i	0.434869	+	0.900494i	$0.356795\pi$
$524$	11.2285	−	15.0826i	0.490521	−	0.658884i
$525$		0			0
$526$	3.03623	−	3.21822i	0.132386	−	0.140321i
$527$	23.7507	−	25.1743i	1.03460	−	1.09661i
$528$		0			0
$529$	−11.5612	+	15.5293i	−0.502660	+	0.675189i
$530$	−34.6658	+	12.6173i	−1.50578	+	0.548061i
$531$		0			0
$532$	−8.83053	−	3.21405i	−0.382852	−	0.139347i
$533$	18.0532	−	11.8738i	0.781972	−	0.514311i
$534$		0			0
$535$	−5.05949	−	6.79607i	−0.218741	−	0.293820i
$536$	−1.88291	−	1.23841i	−0.0813293	−	0.0534912i
$537$		0			0
$538$	10.0456	−	33.5545i	0.433095	−	1.44664i
$539$	2.18177	−	3.77894i	0.0939756	−	0.162771i
$540$		0			0
$541$	−14.5703	−	25.2365i	−0.626427	−	1.08500i	−0.988263	−	0.152761i	$-0.951183\pi$
$541$	−14.5703	−	25.2365i	−0.626427	−	1.08500i	0.361836	−	0.932242i	$-0.382150\pi$
$542$	17.0315	−	4.03654i	0.731566	−	0.173384i
$543$		0			0
$544$	33.8456	−	16.9979i	1.45112	−	0.728778i
$545$	−0.170839	+	0.396049i	−0.00731794	+	0.0169649i
$546$		0			0
$547$	1.71924	+	29.5182i	0.0735094	+	1.26211i	0.810311	+	0.586000i	$0.199298\pi$
$547$	1.71924	+	29.5182i	0.0735094	+	1.26211i	−0.736802	+	0.676109i	$0.763665\pi$
$548$	−2.79518	−	15.8523i	−0.119404	−	0.677176i
$549$		0			0
$550$	−0.123902	+	0.702682i	−0.00528319	+	0.0299625i
$551$	4.28494	+	0.500838i	0.182545	+	0.0213364i
$552$		0			0
$553$	−9.46020	−	31.5993i	−0.402288	−	1.34374i
$554$	−30.9657	−	7.33900i	−1.31561	−	0.311804i
$555$		0			0
$556$	4.66304	+	10.8101i	0.197757	+	0.458452i
$557$	26.7348	+	22.4332i	1.13279	+	0.950525i	0.999179	−	0.0405084i	$-0.0128978\pi$
$557$	26.7348	+	22.4332i	1.13279	+	0.950525i	0.133613	+	0.991034i	$0.457342\pi$
$558$		0			0
$559$	15.8748	−	13.3206i	0.671434	−	0.563400i
$560$	−46.1720	−	23.1884i	−1.95112	−	0.979890i
$561$		0			0
$562$	13.0652	−	1.52710i	0.551122	−	0.0644169i
$563$	2.36224	−	40.5581i	0.0995566	−	1.70932i	−0.466143	−	0.884709i	$-0.654357\pi$
$563$	2.36224	−	40.5581i	0.0995566	−	1.70932i	0.565699	−	0.824611i	$-0.308606\pi$
$564$		0			0
$565$	3.40735	+	3.61158i	0.143348	+	0.151940i
$566$	42.8973			1.80311
$567$		0			0
$568$	−1.84525			−0.0774249
$569$	−20.7255	−	21.9678i	−0.868859	−	0.920937i	0.128635	−	0.991692i	$-0.458941\pi$
$569$	−20.7255	−	21.9678i	−0.868859	−	0.920937i	−0.997494	+	0.0707552i	$0.977459\pi$
$570$		0			0
$571$	2.27410	−	39.0448i	0.0951680	−	1.63397i	−0.526134	−	0.850401i	$-0.676359\pi$
$571$	2.27410	−	39.0448i	0.0951680	−	1.63397i	0.621302	−	0.783571i	$-0.286604\pi$
$572$	−1.78061	+	0.208124i	−0.0744512	+	0.00870210i
$573$		0			0
$574$	−49.4220	−	24.8207i	−2.06284	−	1.03600i
$575$	1.71561	−	1.43956i	0.0715457	−	0.0600340i
$576$		0			0
$577$	−15.1407	−	12.7046i	−0.630316	−	0.528898i	0.270711	−	0.962661i	$-0.412741\pi$
$577$	−15.1407	−	12.7046i	−0.630316	−	0.528898i	−0.901027	+	0.433763i	$0.857186\pi$
$578$	6.82362	+	15.8189i	0.283825	+	0.657981i
$579$		0			0
$580$	−13.8923	−	3.29252i	−0.576844	−	0.136715i
$581$	15.7763	+	52.6966i	0.654512	+	2.18622i
$582$		0			0
$583$	−2.45032	−	0.286401i	−0.101482	−	0.0118615i
$584$	0.480450	−	2.72477i	0.0198812	−	0.112752i
$585$		0			0
$586$	4.20225	+	23.8321i	0.173593	+	0.984496i
$587$	−0.799246	−	13.7225i	−0.0329884	−	0.566389i	−0.973792	−	0.227438i	$-0.926965\pi$
$587$	−0.799246	−	13.7225i	−0.0329884	−	0.566389i	0.940804	−	0.338951i	$-0.110072\pi$
$588$		0			0
$589$	−3.34616	+	7.75727i	−0.137876	+	0.319633i
$590$	16.8555	−	8.46517i	0.693932	−	0.348506i
$591$		0			0
$592$	−37.9387	+	8.99163i	−1.55927	+	0.369554i
$593$	10.7816	+	18.6743i	0.442747	+	0.766860i	0.997892	−	0.0648932i	$-0.0206707\pi$
$593$	10.7816	+	18.6743i	0.442747	+	0.766860i	−0.555145	+	0.831753i	$0.687337\pi$
$594$		0			0
$595$	28.8473	−	49.9649i	1.18262	−	2.04836i
$596$	−10.1075	+	33.7613i	−0.414018	+	1.38292i
$597$		0			0
$598$	10.3722	+	6.82194i	0.424153	+	0.278970i
$599$	9.88790	+	13.2818i	0.404009	+	0.542678i	0.956840	−	0.290616i	$-0.0938601\pi$
$599$	9.88790	+	13.2818i	0.404009	+	0.542678i	−0.552831	+	0.833293i	$0.686453\pi$
$600$		0			0
$601$	15.4638	−	10.1707i	0.630780	−	0.414870i	−0.193463	−	0.981108i	$-0.561972\pi$
$601$	15.4638	−	10.1707i	0.630780	−	0.414870i	0.824242	+	0.566237i	$0.191601\pi$
$602$	−49.8411	−	18.1407i	−2.03137	−	0.739359i
$603$		0			0
$604$	31.4224	−	11.4368i	1.27856	−	0.465357i
$605$	16.1717	−	21.7224i	0.657474	−	0.883141i
$606$		0			0
$607$	−15.0028	+	15.9020i	−0.608945	+	0.645444i	−0.956334	−	0.292278i	$-0.905587\pi$
$607$	−15.0028	+	15.9020i	−0.608945	+	0.645444i	0.347389	+	0.937721i	$0.387068\pi$
$608$	−6.34430	+	6.72456i	−0.257295	+	0.272717i
$609$		0			0
$610$	−6.97863	+	9.37393i	−0.282557	+	0.379539i
$611$	−13.0371	+	4.74513i	−0.527427	+	0.191968i
$612$		0			0
$613$	13.7105	+	4.99021i	0.553762	+	0.201553i	0.603717	−	0.797199i	$-0.293686\pi$
$613$	13.7105	+	4.99021i	0.553762	+	0.201553i	−0.0499554	+	0.998751i	$0.515908\pi$
$614$	−1.34899	+	0.887243i	−0.0544407	+	0.0358062i
$615$		0			0
$616$	−0.565204	−	0.759201i	−0.0227727	−	0.0305891i
$617$	36.4343	+	23.9632i	1.46679	+	0.964723i	0.996620	+	0.0821465i	$0.0261776\pi$
$617$	36.4343	+	23.9632i	1.46679	+	0.964723i	0.470169	+	0.882576i	$0.344193\pi$
$618$		0			0
$619$	−1.86037	+	6.21407i	−0.0747746	+	0.249765i	−0.987202	−	0.159474i	$-0.949020\pi$
$619$	−1.86037	+	6.21407i	−0.0747746	+	0.249765i	0.912428	+	0.409238i	$0.134206\pi$
$620$	13.9792	−	24.2127i	0.561418	−	0.972405i
$621$		0			0
$622$	−5.19078	−	8.99070i	−0.208131	−	0.360494i
$623$	16.5510	−	3.92267i	0.663103	−	0.157158i
$624$		0			0
$625$	−26.3545	+	13.2357i	−1.05418	+	0.529430i
$626$	−16.2053	+	37.5680i	−0.647693	+	1.50152i
$627$		0			0
$628$	0.779202	+	13.3784i	0.0310935	+	0.533856i
$629$	−7.56022	−	42.8761i	−0.301446	−	1.70958i
$630$		0			0
$631$	−2.98327	+	16.9189i	−0.118762	+	0.673533i	0.866057	+	0.499946i	$0.166647\pi$
$631$	−2.98327	+	16.9189i	−0.118762	+	0.673533i	−0.984819	+	0.173587i	$0.944464\pi$
$632$	−4.70676	−	0.550141i	−0.187225	−	0.0218834i
$633$		0			0
$634$	2.18828	+	7.30935i	0.0869076	+	0.290292i
$635$	7.69462	+	1.82366i	0.305352	+	0.0723697i
$636$		0			0
$637$	−18.5032	−	42.8952i	−0.733122	−	1.69957i
$638$	−1.61364	−	1.35401i	−0.0638848	−	0.0536057i
$639$		0			0
$640$	−9.81485	+	8.23563i	−0.387966	+	0.325542i
$641$	28.7417	+	14.4346i	1.13523	+	0.570133i	0.914252	−	0.405146i	$-0.132779\pi$
$641$	28.7417	+	14.4346i	1.13523	+	0.570133i	0.220976	+	0.975279i	$0.429076\pi$
$642$		0			0
$643$	−20.0915	+	2.34836i	−0.792333	+	0.0926104i	−0.502625	−	0.864505i	$-0.667632\pi$
$643$	−20.0915	+	2.34836i	−0.792333	+	0.0926104i	−0.289708	+	0.957115i	$0.593558\pi$
$644$	0.837395	−	14.3775i	0.0329980	−	0.566554i
$645$		0			0
$646$	−8.33226	−	8.83168i	−0.327829	−	0.347478i
$647$	47.4222			1.86436			0.932179	−	0.361999i	$-0.117906\pi$
$647$	47.4222			1.86436			0.932179	+	0.361999i	$0.117906\pi$
$648$		0			0
$649$	1.26136			0.0495125
$650$	5.24214	+	5.55634i	0.205614	+	0.217938i
$651$		0			0
$652$	0.884643	−	15.1887i	0.0346453	−	0.594837i
$653$	3.61557	−	0.422600i	0.141488	−	0.0165376i	−0.0450539	−	0.998985i	$-0.514346\pi$
$653$	3.61557	−	0.422600i	0.141488	−	0.0165376i	0.186542	+	0.982447i	$0.440272\pi$
$654$		0			0
$655$	−25.1820	−	12.6469i	−0.983942	−	0.494154i
$656$	−22.2190	+	18.6440i	−0.867508	+	0.727925i
$657$		0			0
$658$	27.2018	+	22.8250i	1.06044	+	0.889812i
$659$	−5.82593	−	13.5060i	−0.226946	−	0.526120i	0.766254	−	0.642537i	$-0.222118\pi$
$659$	−5.82593	−	13.5060i	−0.226946	−	0.526120i	−0.993200	+	0.116417i	$0.962859\pi$
$660$		0			0
$661$	−2.19525	−	0.520283i	−0.0853852	−	0.0202367i	0.187701	−	0.982226i	$-0.439896\pi$
$661$	−2.19525	−	0.520283i	−0.0853852	−	0.0202367i	−0.273086	+	0.961990i	$0.588044\pi$
$662$	−4.18476	−	13.9781i	−0.162645	−	0.543273i
$663$		0			0
$664$	7.84923	+	0.917444i	0.304609	+	0.0356037i
$665$	−2.44550	+	13.8691i	−0.0948326	+	0.537822i
$666$		0			0
$667$	1.14810	+	6.51120i	0.0444546	+	0.252115i
$668$	−1.57636	−	27.0650i	−0.0609912	−	1.04718i
$669$		0			0
$670$	6.48510	−	15.0342i	0.250541	−	0.580820i
$671$	−0.698383	+	0.350741i	−0.0269608	+	0.0135402i
$672$		0			0
$673$	38.5309	−	9.13198i	1.48526	−	0.352012i	0.593613	−	0.804751i	$-0.297701\pi$
$673$	38.5309	−	9.13198i	1.48526	−	0.352012i	0.891643	+	0.452739i	$0.149553\pi$
$674$	5.11805	+	8.86473i	0.197140	+	0.341457i
$675$		0			0
$676$	1.18051	−	2.04470i	0.0454042	−	0.0786423i
$677$	−6.75371	+	22.5590i	−0.259566	+	0.867011i	0.724510	+	0.689264i	$0.242066\pi$
$677$	−6.75371	+	22.5590i	−0.259566	+	0.867011i	−0.984076	+	0.177747i	$0.943119\pi$
$678$		0			0
$679$	55.6356	+	36.5921i	2.13510	+	1.40428i
$680$	−4.94967	−	6.64856i	−0.189811	−	0.254961i
$681$		0			0
$682$	3.44640	−	2.26674i	0.131970	−	0.0867978i
$683$	16.8551	+	6.13475i	0.644942	+	0.234740i	0.643722	−	0.765260i	$-0.277389\pi$
$683$	16.8551	+	6.13475i	0.644942	+	0.234740i	0.00122025	+	0.999999i	$0.499612\pi$
$684$		0			0
$685$	−22.6685	+	8.25067i	−0.866120	+	0.315242i
$686$	−34.9993	+	47.0122i	−1.33628	+	1.79493i
$687$		0			0
$688$	−19.0892	+	20.2334i	−0.727770	+	0.771391i
$689$	−18.1247	+	19.2110i	−0.690494	+	0.731881i
$690$		0			0
$691$	−26.5394	+	35.6486i	−1.00961	+	1.35614i	−0.0762877	+	0.997086i	$0.524307\pi$
$691$	−26.5394	+	35.6486i	−1.00961	+	1.35614i	−0.933318	+	0.359050i	$0.883101\pi$
$692$	18.3905	−	6.69361i	0.699103	−	0.254453i
$693$		0			0
$694$	23.7794	+	8.65500i	0.902655	+	0.328539i
$695$	14.7409	−	9.69523i	0.559154	−	0.367761i
$696$		0			0
$697$	−19.3409	−	25.9793i	−0.732588	−	0.984036i
$698$	−28.9756	−	19.0576i	−1.09674	−	0.721340i
$699$		0			0
$700$	2.54157	−	8.48944i	0.0960623	−	0.320871i
$701$	−15.1089	+	26.1694i	−0.570656	+	0.988405i	0.425843	+	0.904797i	$0.359978\pi$
$701$	−15.1089	+	26.1694i	−0.570656	+	0.988405i	−0.996499	+	0.0836077i	$0.973356\pi$
$702$		0			0
$703$	5.31371	+	9.20362i	0.200410	+	0.347121i
$704$	1.56782	−	0.371581i	0.0590895	−	0.0140045i
$705$		0			0
$706$	12.1925	−	6.12330i	0.458870	−	0.230453i
$707$	31.9791	−	74.1359i	1.20270	−	2.78817i
$708$		0			0
$709$	2.59739	+	44.5955i	0.0975470	+	1.67482i	0.592249	+	0.805755i	$0.298240\pi$
$709$	2.59739	+	44.5955i	0.0975470	+	1.67482i	−0.494702	+	0.869063i	$0.664723\pi$
$710$	−2.32793	−	13.2023i	−0.0873657	−	0.495475i
$711$		0			0
$712$	0.424341	−	2.40656i	0.0159028	−	0.0901895i
$713$	−12.8598	−	1.50310i	−0.481605	−	0.0562915i
$714$		0			0
$715$	0.770544	+	2.57380i	0.0288167	+	0.0962546i
$716$	10.2053	+	2.41871i	0.381392	+	0.0903915i
$717$		0			0
$718$	10.1568	+	23.5462i	0.379049	+	0.878735i
$719$	−36.4084	−	30.5503i	−1.35780	−	1.13933i	−0.976654	−	0.214819i	$-0.931084\pi$
$719$	−36.4084	−	30.5503i	−1.35780	−	1.13933i	−0.381149	−	0.924513i	$-0.624472\pi$
$720$		0			0
$721$	−49.7141	+	41.7151i	−1.85145	+	1.55355i
$722$	−29.8253	−	14.9788i	−1.10998	−	0.557455i
$723$		0			0
$724$	28.2403	−	3.30082i	1.04954	−	0.122674i
$725$	−0.236548	+	4.06138i	−0.00878518	+	0.150836i
$726$		0			0
$727$	0.189712	+	0.201083i	0.00703601	+	0.00745774i	0.730882	−	0.682504i	$-0.239109\pi$
$727$	0.189712	+	0.201083i	0.00703601	+	0.00745774i	−0.723846	+	0.689961i	$0.757627\pi$
$728$	−10.1330			−0.375555
$729$		0			0
$730$	20.1012			0.743980
$731$	−21.3159	−	22.5935i	−0.788397	−	0.835652i
$732$		0			0
$733$	0.679124	−	11.6601i	0.0250840	−	0.430676i	−0.962265	−	0.272114i	$-0.912277\pi$
$733$	0.679124	−	11.6601i	0.0250840	−	0.430676i	0.987349	−	0.158562i	$-0.0506858\pi$
$734$	−34.6969	+	4.05549i	−1.28069	+	0.149691i
$735$		0			0
$736$	−12.6615	−	6.35882i	−0.466708	−	0.234389i
$737$	0.838768	−	0.703810i	0.0308964	−	0.0259252i
$738$		0			0
$739$	9.08171	+	7.62046i	0.334076	+	0.280323i	0.794358	−	0.607450i	$-0.207807\pi$
$739$	9.08171	+	7.62046i	0.334076	+	0.280323i	−0.460282	+	0.887773i	$0.652252\pi$
$740$	−13.9303	−	32.2940i	−0.512086	−	1.18715i
$741$		0			0
$742$	65.7767	+	15.5894i	2.41474	+	0.572304i
$743$	−11.1596	−	37.2756i	−0.409405	−	1.36751i	−0.875690	−	0.482874i	$-0.839593\pi$
$743$	−11.1596	−	37.2756i	−0.409405	−	1.36751i	0.466285	−	0.884635i	$-0.345592\pi$
$744$		0			0
$745$	52.4576	+	6.13142i	1.92190	+	0.224638i
$746$	10.6491	−	60.3941i	0.389892	−	2.21119i
$747$		0			0
$748$	0.466615	+	2.64630i	0.0170611	+	0.0967584i
$749$	0.902718	+	15.4991i	0.0329846	+	0.566324i
$750$		0			0
$751$	−16.1607	+	37.4647i	−0.589712	+	1.36711i	0.318231	+	0.948013i	$0.396911\pi$
$751$	−16.1607	+	37.4647i	−0.589712	+	1.36711i	−0.907943	+	0.419093i	$0.862348\pi$
$752$	16.6423	−	8.35806i	0.606881	−	0.304787i
$753$		0			0
$754$	−21.9437	+	5.20076i	−0.799144	+	0.189401i
$755$	−25.0565	−	43.3991i	−0.911899	−	1.57945i
$756$		0			0
$757$	−14.1174	+	24.4520i	−0.513104	+	0.888723i	0.486780	+	0.873524i	$0.338171\pi$
$757$	−14.1174	+	24.4520i	−0.513104	+	0.888723i	−0.999885	+	0.0151982i	$0.995162\pi$
$758$	7.68086	−	25.6559i	0.278982	−	0.931863i
$759$		0			0
$760$	1.69040	+	1.11180i	0.0613174	+	0.0403291i
$761$	18.5778	+	24.9544i	0.673446	+	0.904595i	0.999164	−	0.0408716i	$-0.0130135\pi$
$761$	18.5778	+	24.9544i	0.673446	+	0.904595i	−0.325718	+	0.945467i	$0.605606\pi$
$762$		0			0
$763$	0.660342	−	0.434314i	0.0239060	−	0.0157232i
$764$	11.9825	+	4.36126i	0.433510	+	0.157785i
$765$		0			0
$766$	12.5171	−	4.55584i	0.452260	−	0.164609i
$767$	8.06401	−	10.8318i	0.291174	−	0.391115i
$768$		0			0
$769$	10.8721	−	11.5237i	0.392057	−	0.415556i	−0.501037	−	0.865426i	$-0.667048\pi$
$769$	10.8721	−	11.5237i	0.392057	−	0.415556i	0.893094	+	0.449869i	$0.148529\pi$
$770$	4.71886	−	5.00170i	0.170056	−	0.180249i
$771$		0			0
$772$	9.41562	−	12.6474i	0.338876	−	0.455189i
$773$	30.9986	−	11.2826i	1.11494	−	0.405805i	0.282137	−	0.959374i	$-0.408957\pi$
$773$	30.9986	−	11.2826i	1.11494	−	0.405805i	0.832803	+	0.553569i	$0.186734\pi$
$774$		0			0
$775$	−7.48629	−	2.72479i	−0.268916	−	0.0978773i
$776$	7.99291	−	5.25702i	0.286929	−	0.188716i
$777$		0			0
$778$	8.46710	+	11.3733i	0.303560	+	0.407752i
$779$	6.60526	+	4.34435i	0.236658	+	0.155652i
$780$		0			0
$781$	0.257121	−	0.858844i	0.00920051	−	0.0307318i
$782$	9.30410	−	16.1152i	0.332714	−	0.576277i
$783$		0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.31250 - 1.39117i) q^{2} +(-0.0964037 + 1.65519i) q^{4} +(2.46793 - 0.288460i) q^{5} +(-4.06877 - 2.04341i) q^{7} +(-0.501084 + 0.420459i) q^{8} +O(q^{10})\)	\(q+(-1.31250 - 1.39117i) q^{2} +(-0.0964037 + 1.65519i) q^{4} +(2.46793 - 0.288460i) q^{5} +(-4.06877 - 2.04341i) q^{7} +(-0.501084 + 0.420459i) q^{8} +(-3.64045 - 3.05470i) q^{10} +(-0.125874 - 0.291810i) q^{11} +(-3.31064 - 0.784636i) q^{13} +(2.49752 + 8.34231i) q^{14} +(4.53616 + 0.530202i) q^{16} +(-0.885565 + 5.02229i) q^{17} +(-0.216164 - 1.22593i) q^{19} +(0.239538 + 4.11270i) q^{20} +(-0.240746 + 0.558112i) q^{22} +(1.70487 - 0.856218i) q^{23} +(1.14226 - 0.270720i) q^{25} +(3.25365 + 5.63548i) q^{26} +(3.77448 - 6.53759i) q^{28} +(-0.993943 + 3.32000i) q^{29} +(-5.67009 - 3.72928i) q^{31} +(-4.43488 - 5.95708i) q^{32} +(8.14914 - 5.35978i) q^{34} +(-10.6309 - 3.86933i) q^{35} +(-8.02231 + 2.91988i) q^{37} +(-1.42176 + 1.90975i) q^{38} +(-1.11536 + 1.18221i) q^{40} +(-4.35826 + 4.61948i) q^{41} +(-3.63719 + 4.88559i) q^{43} +(0.495135 - 0.180214i) q^{44} +(-3.42878 - 1.24797i) q^{46} +(3.40689 - 2.24075i) q^{47} +(8.19925 + 11.0135i) q^{49} +(-1.87583 - 1.23375i) q^{50} +(1.61788 - 5.40409i) q^{52} +(3.88136 - 6.72271i) q^{53} +(-0.394825 - 0.683857i) q^{55} +(2.89797 - 0.686831i) q^{56} +(5.92322 - 2.97475i) q^{58} +(-1.57205 + 3.64441i) q^{59} +(-0.142985 - 2.45496i) q^{61} +(2.25394 + 12.7827i) q^{62} +(-0.880398 + 4.99299i) q^{64} +(-8.39677 - 0.981441i) q^{65} +(0.988137 + 3.30061i) q^{67} +(-8.22746 - 1.94994i) q^{68} +(8.57015 + 19.8678i) q^{70} +(2.16099 + 1.81328i) q^{71} +(-3.24023 + 2.71887i) q^{73} +(14.5913 + 7.32803i) q^{74} +(2.04998 - 0.239609i) q^{76} +(-0.0841338 + 1.44452i) q^{77} +(4.97152 + 5.26950i) q^{79} +11.3479 q^{80} +12.1467 q^{82} +(-8.29076 - 8.78769i) q^{83} +(-0.736786 + 12.6501i) q^{85} +(11.5705 - 1.35239i) q^{86} +(0.185768 + 0.0932961i) q^{88} +(-2.86182 + 2.40135i) q^{89} +(11.8669 + 9.95751i) q^{91} +(1.25285 + 2.90442i) q^{92} +(-7.58878 - 1.79857i) q^{94} +(-0.887111 - 2.96316i) q^{95} +(-14.5265 - 1.69791i) q^{97} +(4.56012 - 25.8617i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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Database

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