LMFDB - Embedded newform 729.2.g.a.514.6

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			514.6
Character	$\chi$	$=$	729.514
Dual form			729.2.g.a.217.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0484354 + 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(1.17364 + 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(0.478230 + 2.71217i) q^{8} +O(q^{10})$	\(q+(0.0484354 + 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(1.17364 + 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(0.478230 + 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(1.49146 + 1.58086i) q^{11} +(4.07045 - 2.04426i) q^{13} +(-0.915130 - 0.601890i) q^{14} +(0.309479 - 0.0733479i) q^{16} +(-3.54217 + 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(1.56469 + 0.182886i) q^{20} +(-1.24241 + 1.31687i) q^{22} +(3.60284 + 4.83945i) q^{23} +(-3.16810 - 1.59108i) q^{25} +(1.89717 + 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(-3.47381 + 2.28476i) q^{29} +(2.95363 - 6.84728i) q^{31} +(1.65571 + 5.53044i) q^{32} +(-1.24371 - 2.88323i) q^{34} +(-1.21492 + 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(0.636923 - 2.12747i) q^{38} +(-0.193143 + 3.31614i) q^{40} +(0.336547 - 5.77829i) q^{41} +(1.44983 - 4.84276i) q^{43} +(2.17451 + 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(1.18743 + 2.75276i) q^{47} +(1.51175 + 5.04961i) q^{49} +(1.16970 - 2.71167i) q^{50} +(4.97047 - 3.26913i) q^{52} +(6.22987 - 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(-3.23606 - 1.62521i) q^{56} +(-2.06827 - 2.77817i) q^{58} +(-7.48542 + 7.93408i) q^{59} +(-11.7134 - 1.36910i) q^{61} +(5.83728 + 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(5.34588 - 1.26700i) q^{65} +(0.693545 + 0.456152i) q^{67} +(-4.39962 + 2.20957i) q^{68} +(-0.906613 - 0.960954i) q^{70} +(-1.25916 + 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(-4.85605 + 6.52281i) q^{74} +(-3.38811 - 0.802996i) q^{76} +(-2.83844 + 0.331766i) q^{77} +(0.668640 + 11.4801i) q^{79} +0.383620 q^{80} +4.82155 q^{82} +(-0.277632 - 4.76675i) q^{83} +(-4.51585 + 0.527827i) q^{85} +(4.09748 + 0.971120i) q^{86} +(-3.57430 + 4.80112i) q^{88} +(-0.578632 - 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(5.40761 + 5.73174i) q^{92} +(-2.23169 + 1.12080i) q^{94} +(-2.68654 - 1.76697i) q^{95} +(1.32651 - 0.314388i) q^{97} +(-4.12605 + 1.50176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	0.0484354	+	0.831603i	0.0342490	+	0.588032i	0.971155	+	0.238450i	$0.0766394\pi$
$2$	0.0484354	+	0.831603i	0.0342490	+	0.588032i	−0.936906	+	0.349582i	$0.886324\pi$
$3$		0			0
$3$		0			0
$4$	1.29726	−	0.151628i	0.648629	−	0.0758139i
$5$	1.17364	+	0.278158i	0.524868	+	0.124396i	0.484504	−	0.874789i	$-0.339000\pi$
$5$	1.17364	+	0.278158i	0.524868	+	0.124396i	0.0403642	+	0.999185i	$0.487148\pi$
$6$		0			0
$7$	−0.785201	+	1.05471i	−0.296778	+	0.398642i	−0.925353	−	0.379107i	$-0.876231\pi$
$7$	−0.785201	+	1.05471i	−0.296778	+	0.398642i	0.628575	+	0.777749i	$0.283639\pi$
$8$	0.478230	+	2.71217i	0.169080	+	0.958899i
$9$		0			0
$10$	−0.174471	+	0.989477i	−0.0551727	+	0.312900i
$11$	1.49146	+	1.58086i	0.449693	+	0.476646i	0.912069	−	0.410038i	$-0.134484\pi$
$11$	1.49146	+	1.58086i	0.449693	+	0.476646i	−0.462376	+	0.886684i	$0.653003\pi$
$12$		0			0
$13$	4.07045	−	2.04426i	1.12894	−	0.566975i	0.216540	−	0.976274i	$-0.430523\pi$
$13$	4.07045	−	2.04426i	1.12894	−	0.566975i	0.912401	+	0.409298i	$0.134226\pi$
$14$	−0.915130	−	0.601890i	−0.244579	−	0.160862i
$15$		0			0
$16$	0.309479	−	0.0733479i	0.0773698	−	0.0183370i
$17$	−3.54217	+	1.28924i	−0.859102	+	0.312688i	−0.733746	−	0.679424i	$-0.762230\pi$
$17$	−3.54217	+	1.28924i	−0.859102	+	0.312688i	−0.125356	+	0.992112i	$0.540007\pi$
$18$		0			0
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	0.0382728	−	0.999267i	$-0.487814\pi$
$19$	−2.50517	−	0.911807i	−0.574725	−	0.209183i	−0.612998	+	0.790084i	$0.710037\pi$
$20$	1.56469	+	0.182886i	0.349876	+	0.0408947i
$21$		0			0
$22$	−1.24241	+	1.31687i	−0.264882	+	0.280758i
$23$	3.60284	+	4.83945i	0.751244	+	1.00910i	0.999187	+	0.0403213i	$0.0128382\pi$
$23$	3.60284	+	4.83945i	0.751244	+	1.00910i	−0.247943	+	0.968775i	$0.579754\pi$
$24$		0			0
$25$	−3.16810	−	1.59108i	−0.633620	−	0.318216i
$26$	1.89717	+	3.28599i	0.372065	+	0.644435i
$27$		0			0
$28$	−0.858686	+	1.48729i	−0.162276	+	0.281071i
$29$	−3.47381	+	2.28476i	−0.645070	+	0.424269i	−0.829446	−	0.558587i	$-0.811344\pi$
$29$	−3.47381	+	2.28476i	−0.645070	+	0.424269i	0.184376	+	0.982856i	$0.440974\pi$
$30$		0			0
$31$	2.95363	−	6.84728i	0.530488	−	1.22981i	−0.416675	−	0.909055i	$-0.636805\pi$
$31$	2.95363	−	6.84728i	0.530488	−	1.22981i	0.947163	−	0.320753i	$-0.103936\pi$
$32$	1.65571	+	5.53044i	0.292690	+	0.977654i
$33$		0			0
$34$	−1.24371	−	2.88323i	−0.213294	−	0.494470i
$35$	−1.21492	+	1.01944i	−0.205359	+	0.172317i
$36$		0			0
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.998277	+	0.0586711i	$0.0186863\pi$
$37$	7.47819	+	6.27494i	1.22941	+	1.03159i	0.231129	+	0.972923i	$0.425758\pi$
$38$	0.636923	−	2.12747i	0.103322	−	0.345121i
$39$		0			0
$40$	−0.193143	+	3.31614i	−0.0305387	+	0.524328i
$41$	0.336547	−	5.77829i	0.0525599	−	0.902418i	−0.864242	−	0.503076i	$-0.832202\pi$
$41$	0.336547	−	5.77829i	0.0525599	−	0.902418i	0.916802	−	0.399342i	$-0.130761\pi$
$42$		0			0
$43$	1.44983	−	4.84276i	0.221097	−	0.738514i	−0.773416	−	0.633899i	$-0.781454\pi$
$43$	1.44983	−	4.84276i	0.221097	−	0.738514i	0.994513	−	0.104616i	$-0.0333612\pi$
$44$	2.17451	+	1.82463i	0.327820	+	0.275074i
$45$		0			0
$46$	−3.85000	+	3.23053i	−0.567652	+	0.476316i
$47$	1.18743	+	2.75276i	0.173204	+	0.401531i	0.982601	−	0.185730i	$-0.0594651\pi$
$47$	1.18743	+	2.75276i	0.173204	+	0.401531i	−0.809397	+	0.587262i	$0.800206\pi$
$48$		0			0
$49$	1.51175	+	5.04961i	0.215965	+	0.721373i
$50$	1.16970	−	2.71167i	0.165420	−	0.383488i
$51$		0			0
$52$	4.97047	−	3.26913i	0.689280	−	0.453346i
$53$	6.22987	−	10.7905i	0.855739	−	1.48218i	−0.0202187	−	0.999796i	$-0.506436\pi$
$53$	6.22987	−	10.7905i	0.855739	−	1.48218i	0.875958	−	0.482388i	$-0.160230\pi$
$54$		0			0
$55$	1.31071	+	2.27022i	0.176737	+	0.306117i
$56$	−3.23606	−	1.62521i	−0.432436	−	0.217178i
$57$		0			0
$58$	−2.06827	−	2.77817i	−0.271577	−	0.364791i
$59$	−7.48542	+	7.93408i	−0.974518	+	1.03293i	0.0249289	+	0.999689i	$0.492064\pi$
$59$	−7.48542	+	7.93408i	−0.974518	+	1.03293i	−0.999447	+	0.0332400i	$0.989417\pi$
$60$		0			0
$61$	−11.7134	−	1.36910i	−1.49975	−	0.175295i	−0.673746	−	0.738963i	$-0.735316\pi$
$61$	−11.7134	−	1.36910i	−1.49975	−	0.175295i	−0.826001	+	0.563668i	$0.809390\pi$
$62$	5.83728	+	2.12460i	0.741336	+	0.269824i
$63$		0			0
$64$	−3.92120	+	1.42720i	−0.490150	+	0.178400i
$65$	5.34588	−	1.26700i	0.663075	−	0.157152i
$66$		0			0
$67$	0.693545	+	0.456152i	0.0847300	+	0.0557278i	0.591167	−	0.806549i	$-0.298667\pi$
$67$	0.693545	+	0.456152i	0.0847300	+	0.0557278i	−0.506437	+	0.862277i	$0.669038\pi$
$68$	−4.39962	+	2.20957i	−0.533533	+	0.267950i
$69$		0			0
$70$	−0.906613	−	0.960954i	−0.108361	−	0.114856i
$71$	−1.25916	+	7.14107i	−0.149435	+	0.847489i	0.814263	+	0.580496i	$0.197141\pi$
$71$	−1.25916	+	7.14107i	−0.149435	+	0.847489i	−0.963698	+	0.266993i	$0.913970\pi$
$72$		0			0
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	−0.949028	−	0.315191i	$-0.897931\pi$
$73$	−1.41006	−	7.99685i	−0.165035	−	0.935960i	0.783993	−	0.620769i	$-0.213180\pi$
$74$	−4.85605	+	6.52281i	−0.564505	+	0.758261i
$75$		0			0
$76$	−3.38811	−	0.802996i	−0.388643	−	0.0921100i
$77$	−2.83844	+	0.331766i	−0.323470	+	0.0378082i
$78$		0			0
$79$	0.668640	+	11.4801i	0.0752278	+	1.29161i	0.798898	+	0.601466i	$0.205417\pi$
$79$	0.668640	+	11.4801i	0.0752278	+	1.29161i	−0.723670	+	0.690146i	$0.757546\pi$
$80$	0.383620			0.0428900
$81$		0			0
$82$	4.82155			0.532451
$83$	−0.277632	−	4.76675i	−0.0304740	−	0.523219i	−0.978658	−	0.205497i	$-0.934119\pi$
$83$	−0.277632	−	4.76675i	−0.0304740	−	0.523219i	0.948184	−	0.317722i	$-0.102918\pi$
$84$		0			0
$85$	−4.51585	+	0.527827i	−0.489813	+	0.0572509i
$86$	4.09748	+	0.971120i	0.441842	+	0.104719i
$87$		0			0
$88$	−3.57430	+	4.80112i	−0.381022	+	0.511801i
$89$	−0.578632	−	3.28158i	−0.0613348	−	0.347847i	−0.999995	−	0.00300484i	$-0.999044\pi$
$89$	−0.578632	−	3.28158i	−0.0613348	−	0.347847i	0.938661	−	0.344842i	$-0.112068\pi$
$90$		0			0
$91$	−1.04003	+	5.89829i	−0.109025	+	0.618309i
$92$	5.40761	+	5.73174i	0.563783	+	0.597575i
$93$		0			0
$94$	−2.23169	+	1.12080i	−0.230181	+	0.115601i
$95$	−2.68654	−	1.76697i	−0.275634	−	0.181287i
$96$		0			0
$97$	1.32651	−	0.314388i	0.134686	−	0.0319212i	−0.162720	−	0.986672i	$-0.552027\pi$
$97$	1.32651	−	0.314388i	0.134686	−	0.0319212i	0.297406	+	0.954751i	$0.403879\pi$
$98$	−4.12605	+	1.50176i	−0.416794	+	0.151701i
$99$		0			0
$100$	−4.35110	−	1.58367i	−0.435110	−	0.158367i
$101$	2.29919	+	0.268737i	0.228778	+	0.0267403i	0.229709	−	0.973259i	$-0.426222\pi$
$101$	2.29919	+	0.268737i	0.228778	+	0.0267403i	−0.000931520		1.00000i	$0.500297\pi$
$102$		0			0
$103$	−3.12210	+	3.30923i	−0.307629	+	0.326068i	−0.862682	−	0.505747i	$-0.831217\pi$
$103$	−3.12210	+	3.30923i	−0.307629	+	0.326068i	0.555052	+	0.831815i	$0.312698\pi$
$104$	7.49100	+	10.0622i	0.734553	+	0.986676i
$105$		0			0
$106$	9.27513	+	4.65814i	0.900880	+	0.452439i
$107$	−6.14665	−	10.6463i	−0.594219	−	1.02922i	−0.993657	−	0.112457i	$-0.964128\pi$
$107$	−6.14665	−	10.6463i	−0.594219	−	1.02922i	0.399438	−	0.916760i	$-0.369205\pi$
$108$		0			0
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	−0.570017	−	0.821633i	$-0.693063\pi$
$109$	4.45327	−	7.71330i	0.426546	−	0.738800i	0.996563	+	0.0828329i	$0.0263968\pi$
$110$	−1.82444	+	1.19995i	−0.173953	+	0.114411i
$111$		0			0
$112$	−0.165643	+	0.384003i	−0.0156518	+	0.0362849i
$113$	−4.98772	−	16.6601i	−0.469205	−	1.56725i	−0.785667	−	0.618649i	$-0.787680\pi$
$113$	−4.98772	−	16.6601i	−0.469205	−	1.56725i	0.316462	−	0.948605i	$-0.397505\pi$
$114$		0			0
$115$	2.88231	+	6.68194i	0.268777	+	0.623095i
$116$	−4.16000	+	3.49065i	−0.386246	+	0.324099i
$117$		0			0
$118$	−6.96056	−	5.84061i	−0.640772	−	0.537671i
$119$	1.42154	−	4.74827i	0.130312	−	0.435273i
$120$		0			0
$121$	0.364942	−	6.26581i	0.0331765	−	0.569619i
$122$	0.571205	−	9.80721i	0.0517145	−	0.887903i
$123$		0			0
$124$	2.79338	−	9.33055i	0.250853	−	0.837908i
$125$	−7.89548	−	6.62509i	−0.706193	−	0.592566i
$126$		0			0
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	−0.428915	−	0.903345i	$-0.641104\pi$
$127$	4.35255	−	3.65222i	0.386226	−	0.324082i	0.815141	+	0.579263i	$0.196660\pi$
$128$	3.19633	+	7.40992i	0.282518	+	0.654950i
$129$		0			0
$130$	1.31257	+	4.38428i	0.115120	+	0.384527i
$131$	7.73087	−	17.9222i	0.675449	−	1.56587i	−0.142000	−	0.989867i	$-0.545353\pi$
$131$	7.73087	−	17.9222i	0.675449	−	1.56587i	0.817449	−	0.576001i	$-0.195388\pi$
$132$		0			0
$133$	2.92875	−	1.92627i	0.253955	−	0.167029i
$134$	−0.345745	+	0.598848i	−0.0298678	+	0.0517326i
$135$		0			0
$136$	−5.19062	−	8.99042i	−0.445092	−	0.770922i
$137$	−14.1679	−	7.11536i	−1.21044	−	0.607907i	−0.275019	−	0.961439i	$-0.588684\pi$
$137$	−14.1679	−	7.11536i	−1.21044	−	0.607907i	−0.935422	+	0.353532i	$0.884980\pi$
$138$		0			0
$139$	−6.23388	−	8.37355i	−0.528751	−	0.710236i	0.454855	−	0.890565i	$-0.349691\pi$
$139$	−6.23388	−	8.37355i	−0.528751	−	0.710236i	−0.983606	+	0.180330i	$0.942284\pi$
$140$	−1.42149	+	1.50669i	−0.120138	+	0.127339i
$141$		0			0
$142$	−5.99952	−	0.701243i	−0.503469	−	0.0588470i
$143$	9.30261	+	3.38587i	0.777923	+	0.283141i
$144$		0			0
$145$	−4.71253	+	1.71522i	−0.391354	+	0.142441i
$146$	6.58191	−	1.55994i	0.544722	−	0.129102i
$147$		0			0
$148$	10.6526	+	7.00632i	0.875638	+	0.575916i
$149$	2.60504	−	1.30830i	0.213413	−	0.107180i	−0.338882	−	0.940829i	$-0.610049\pi$
$149$	2.60504	−	1.30830i	0.213413	−	0.107180i	0.552295	+	0.833649i	$0.313752\pi$
$150$		0			0
$151$	8.75633	+	9.28117i	0.712580	+	0.755291i	0.977946	−	0.208857i	$-0.0669743\pi$
$151$	8.75633	+	9.28117i	0.712580	+	0.755291i	−0.265366	+	0.964148i	$0.585493\pi$
$152$	1.27493	−	7.23051i	0.103411	−	0.586472i
$153$		0			0
$154$	−0.413378	−	2.34439i	−0.0333110	−	0.188916i
$155$	5.37113	−	7.21468i	0.431420	−	0.579497i
$156$		0			0
$157$	−1.23639	−	0.293029i	−0.0986743	−	0.0233862i	0.180982	−	0.983486i	$-0.442072\pi$
$157$	−1.23639	−	0.293029i	−0.0986743	−	0.0233862i	−0.279656	+	0.960100i	$0.590221\pi$
$158$	−9.51450	+	1.11209i	−0.756933	+	0.0884728i
$159$		0			0
$160$	0.404868	+	6.95131i	0.0320076	+	0.549549i
$161$	−7.93316			−0.625221
$162$		0			0
$163$	12.3636			0.968391			0.484195	−	0.874960i	$-0.339112\pi$
$163$	12.3636			0.968391			0.484195	+	0.874960i	$0.339112\pi$
$164$	−0.439561	−	7.54697i	−0.0343240	−	0.589320i
$165$		0			0
$166$	3.95060	−	0.461759i	0.306626	−	0.0358394i
$167$	−3.71075	−	0.879464i	−0.287146	−	0.0680550i	0.0845184	−	0.996422i	$-0.473065\pi$
$167$	−3.71075	−	0.879464i	−0.287146	−	0.0680550i	−0.371665	+	0.928367i	$0.621213\pi$
$168$		0			0
$169$	4.62654	−	6.21452i	0.355888	−	0.478040i
$170$	−0.657669	−	3.72983i	−0.0504409	−	0.286065i
$171$		0			0
$172$	1.14650	−	6.50215i	0.0874201	−	0.495784i
$173$	−16.5179	−	17.5080i	−1.25584	−	1.33111i	−0.921364	−	0.388702i	$-0.872924\pi$
$173$	−16.5179	−	17.5080i	−1.25584	−	1.33111i	−0.334471	−	0.942406i	$-0.608558\pi$
$174$		0			0
$175$	4.16572	−	2.09210i	0.314899	−	0.158148i
$176$	0.577529	+	0.379847i	0.0435329	+	0.0286320i
$177$		0			0
$178$	2.70095	−	0.640136i	0.202445	−	0.0479803i
$179$	−5.95691	+	2.16814i	−0.445240	+	0.162054i	−0.554904	−	0.831915i	$-0.687245\pi$
$179$	−5.95691	+	2.16814i	−0.445240	+	0.162054i	0.109664	+	0.993969i	$0.465023\pi$
$180$		0			0
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	0.116532	−	0.993187i	$-0.462822\pi$
$181$	−5.82014	−	2.11836i	−0.432608	−	0.157456i	−0.549140	+	0.835731i	$0.685045\pi$
$182$	−4.95541	−	0.579205i	−0.367320	−	0.0429335i
$183$		0			0
$184$	−11.4025	+	12.0859i	−0.840601	+	0.890985i
$185$	7.03128	+	9.44465i	0.516950	+	0.694385i
$186$		0			0
$187$	−7.32112	−	3.67680i	−0.535373	−	0.268875i
$188$	1.95779	+	3.39100i	0.142787	+	0.247314i
$189$		0			0
$190$	1.33929	−	2.31972i	0.0971625	−	0.168290i
$191$	5.64176	−	3.71064i	0.408223	−	0.268493i	−0.328747	−	0.944418i	$-0.606626\pi$
$191$	5.64176	−	3.71064i	0.408223	−	0.268493i	0.736970	+	0.675925i	$0.236256\pi$
$192$		0			0
$193$	−6.30224	+	14.6102i	−0.453645	+	1.05167i	0.525918	+	0.850535i	$0.323722\pi$
$193$	−6.30224	+	14.6102i	−0.453645	+	1.05167i	−0.979564	+	0.201133i	$0.935538\pi$
$194$	0.325696	+	1.08790i	0.0233836	+	0.0781066i
$195$		0			0
$196$	2.72680	+	6.32143i	0.194771	+	0.451531i
$197$	8.88023	−	7.45140i	0.632690	−	0.530890i	−0.269073	−	0.963120i	$-0.586717\pi$
$197$	8.88023	−	7.45140i	0.632690	−	0.530890i	0.901764	+	0.432229i	$0.142273\pi$
$198$		0			0
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	0.752026	−	0.659133i	$-0.229077\pi$
$199$	3.29385	+	2.76387i	0.233495	+	0.195925i	−0.518531	+	0.855059i	$0.673521\pi$
$200$	2.80021	−	9.35334i	0.198005	−	0.661381i
$201$		0			0
$202$	−0.112120	+	1.92503i	−0.00788875	+	0.135445i
$203$	0.317883	−	5.45785i	0.0223110	−	0.383066i
$204$		0			0
$205$	2.00227	−	6.68803i	0.139844	−	0.467112i
$206$	−2.90318	−	2.43606i	−0.202274	−	0.169728i
$207$		0			0
$208$	1.10978	−	0.931215i	0.0769493	−	0.0645682i
$209$	−2.29493	−	5.32024i	−0.158743	−	0.368009i
$210$		0			0
$211$	−4.09591	−	13.6813i	−0.281974	−	0.941858i	−0.975235	−	0.221172i	$-0.929012\pi$
$211$	−4.09591	−	13.6813i	−0.281974	−	0.941858i	0.693261	−	0.720687i	$-0.256173\pi$
$212$	6.44563	−	14.9426i	0.442687	−	1.02626i
$213$		0			0
$214$	8.55579	−	5.62723i	0.584862	−	0.384669i
$215$	3.04863	−	5.28038i	0.207915	−	0.360119i
$216$		0			0
$217$	4.90269	+	8.49171i	0.332816	+	0.576455i
$218$	6.63010	+	3.32976i	0.449047	+	0.225520i
$219$		0			0
$220$	2.04456	+	2.74633i	0.137844	+	0.185157i
$221$	−11.7827	+	12.4889i	−0.792589	+	0.840095i
$222$		0			0
$223$	20.0537	+	2.34394i	1.34290	+	0.156962i	0.756995	−	0.653421i	$-0.226667\pi$
$223$	20.0537	+	2.34394i	1.34290	+	0.156962i	0.585901	+	0.810383i	$0.300741\pi$
$224$	−7.13306	−	2.59622i	−0.476598	−	0.173467i
$225$		0			0
$226$	13.6130	−	4.95474i	0.905526	−	0.329585i
$227$	−2.65003	+	0.628068i	−0.175889	+	0.0416863i	−0.317616	−	0.948219i	$-0.602882\pi$
$227$	−2.65003	+	0.628068i	−0.175889	+	0.0416863i	0.141728	+	0.989906i	$0.454734\pi$
$228$		0			0
$229$	−1.27542	−	0.838856i	−0.0842821	−	0.0554332i	0.506669	−	0.862141i	$-0.330877\pi$
$229$	−1.27542	−	0.838856i	−0.0842821	−	0.0554332i	−0.590951	+	0.806708i	$0.701247\pi$
$230$	−5.41712	+	2.72058i	−0.357194	+	0.179390i
$231$		0			0
$232$	−7.85794	−	8.32893i	−0.515899	−	0.546821i
$233$	1.13347	−	6.42825i	0.0742563	−	0.421128i	−0.924906	−	0.380197i	$-0.875856\pi$
$233$	1.13347	−	6.42825i	0.0742563	−	0.421128i	0.999162	−	0.0409317i	$-0.0130326\pi$
$234$		0			0
$235$	0.627909	+	3.56105i	0.0409602	+	0.232297i
$236$	−8.50750	+	11.4276i	−0.553791	+	0.743870i
$237$		0			0
$238$	4.01753	+	0.952171i	0.260417	+	0.0617201i
$239$	−16.7833	+	1.96169i	−1.08562	+	0.126891i	−0.640034	−	0.768347i	$-0.721080\pi$
$239$	−16.7833	+	1.96169i	−1.08562	+	0.126891i	−0.445589	+	0.895238i	$0.647006\pi$
$240$		0			0
$241$	0.732563	+	12.5776i	0.0471885	+	0.810196i	0.936017	+	0.351955i	$0.114483\pi$
$241$	0.732563	+	12.5776i	0.0471885	+	0.810196i	−0.888828	+	0.458240i	$0.848480\pi$
$242$	5.22835			0.336091
$243$		0			0
$244$	−15.4029			−0.986070
$245$	0.369667	+	6.34694i	0.0236172	+	0.405491i
$246$		0			0
$247$	−12.0611	+	1.40975i	−0.767432	+	0.0897000i
$248$	19.9835	+	4.73619i	1.26896	+	0.300748i
$249$		0			0
$250$	5.12703	−	6.88679i	0.324262	−	0.435559i
$251$	4.48052	+	25.4103i	0.282808	+	1.60388i	0.713012	+	0.701152i	$0.247331\pi$
$251$	4.48052	+	25.4103i	0.282808	+	1.60388i	−0.430204	+	0.902732i	$0.641558\pi$
$252$		0			0
$253$	−2.27699	+	12.9134i	−0.143153	+	0.811861i
$254$	3.24801	+	3.44269i	0.203799	+	0.216014i
$255$		0			0
$256$	−13.4653	+	6.76252i	−0.841580	+	0.422658i
$257$	12.0914	+	7.95265i	0.754242	+	0.496073i	0.867466	−	0.497497i	$-0.165747\pi$
$257$	12.0914	+	7.95265i	0.754242	+	0.496073i	−0.113224	+	0.993570i	$0.536118\pi$
$258$		0			0
$259$	−12.4901	+	2.96021i	−0.776097	+	0.183938i
$260$	6.74288	−	2.45421i	0.418176	−	0.152204i
$261$		0			0
$262$	15.2786	+	5.56095i	0.943914	+	0.343557i
$263$	−10.3839	−	1.21371i	−0.640300	−	0.0748403i	−0.210253	−	0.977647i	$-0.567429\pi$
$263$	−10.3839	−	1.21371i	−0.640300	−	0.0748403i	−0.430047	+	0.902807i	$0.641503\pi$
$264$		0			0
$265$	10.3131	−	10.9312i	0.633528	−	0.671501i
$266$	1.74375	+	2.34226i	0.106916	+	0.143613i
$267$		0			0
$268$	0.968872	+	0.486586i	0.0591833	+	0.0297230i
$269$	−0.105374	−	0.182513i	−0.00642476	−	0.0111280i	0.862795	−	0.505554i	$-0.168712\pi$
$269$	−0.105374	−	0.182513i	−0.00642476	−	0.0111280i	−0.869220	+	0.494426i	$0.835378\pi$
$270$		0			0
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	−0.638908	−	0.769283i	$-0.720614\pi$
$271$	5.70846	−	9.88735i	0.346765	−	0.600614i	0.985673	+	0.168669i	$0.0539470\pi$
$272$	−1.00166	+	0.658805i	−0.0607348	+	0.0399459i
$273$		0			0
$274$	5.23093	−	12.1267i	0.316012	−	0.732599i
$275$	−2.20983	−	7.38135i	−0.133258	−	0.445112i
$276$		0			0
$277$	−4.41607	−	10.2376i	−0.265336	−	0.615117i	0.732508	−	0.680759i	$-0.238350\pi$
$277$	−4.41607	−	10.2376i	−0.265336	−	0.615117i	−0.997843	+	0.0656416i	$0.979091\pi$
$278$	6.66153	−	5.58969i	0.399532	−	0.335247i
$279$		0			0
$280$	−3.34591	−	2.80755i	−0.199956	−	0.167783i
$281$	−6.22453	+	20.7914i	−0.371325	+	1.24031i	0.544510	+	0.838754i	$0.316716\pi$
$281$	−6.22453	+	20.7914i	−0.371325	+	1.24031i	−0.915834	+	0.401556i	$0.868469\pi$
$282$		0			0
$283$	0.0172412	−	0.296021i	0.00102488	−	0.0175966i	−0.997757	−	0.0669409i	$-0.978676\pi$
$283$	0.0172412	−	0.296021i	0.00102488	−	0.0175966i	0.998782	+	0.0493443i	$0.0157132\pi$
$284$	−0.550676	+	9.45474i	−0.0326766	+	0.561035i
$285$		0			0
$286$	−2.36513	+	7.90008i	−0.139853	+	0.467141i
$287$	5.83015	+	4.89208i	0.344143	+	0.288770i
$288$		0			0
$289$	−2.13795	+	1.79396i	−0.125762	+	0.105527i
$290$	−1.65464	−	3.83588i	−0.0971636	−	0.225250i
$291$		0			0
$292$	−3.04176	−	10.1602i	−0.178005	−	0.594579i
$293$	5.74578	−	13.3202i	0.335672	−	0.778175i	−0.663868	−	0.747850i	$-0.731086\pi$
$293$	5.74578	−	13.3202i	0.335672	−	0.778175i	0.999540	−	0.0303252i	$-0.00965431\pi$
$294$		0			0
$295$	−10.9921	+	7.22964i	−0.639986	+	0.420926i
$296$	−13.4425	+	23.2830i	−0.781327	+	1.35330i
$297$		0			0
$298$	1.21416	+	2.10299i	0.0703346	+	0.121823i
$299$	24.5583	+	12.3336i	1.42024	+	0.713273i
$300$		0			0
$301$	3.96929	+	5.33168i	0.228786	+	0.307313i
$302$	−7.29413	+	7.73133i	−0.419730	+	0.444888i
$303$		0			0
$304$	−0.842177	−	0.0984364i	−0.0483022	−	0.00564571i
$305$	−13.3665	−	4.86501i	−0.765364	−	0.278570i
$306$		0			0
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	−0.441620	−	0.897202i	$-0.645596\pi$
$307$	−3.56052	+	1.29592i	−0.203210	+	0.0739622i	0.238410	+	0.971165i	$0.423374\pi$
$308$	−3.63189	+	0.860773i	−0.206946	+	0.0490471i
$309$		0			0
$310$	6.25990	+	4.11720i	0.355539	+	0.233841i
$311$	−11.0181	+	5.53348i	−0.624777	+	0.313775i	−0.732873	−	0.680366i	$-0.761821\pi$
$311$	−11.0181	+	5.53348i	−0.624777	+	0.313775i	0.108096	+	0.994141i	$0.465525\pi$
$312$		0			0
$313$	−4.67044	−	4.95038i	−0.263989	−	0.279812i	0.581797	−	0.813334i	$-0.302350\pi$
$313$	−4.67044	−	4.95038i	−0.263989	−	0.279812i	−0.845786	+	0.533522i	$0.820868\pi$
$314$	0.183799	−	1.04238i	0.0103724	−	0.0588246i
$315$		0			0
$316$	2.60810	+	14.7913i	0.146717	+	0.832074i
$317$	8.91947	−	11.9809i	0.500967	−	0.672916i	−0.477663	−	0.878543i	$-0.658516\pi$
$317$	8.91947	−	11.9809i	0.500967	−	0.672916i	0.978630	+	0.205627i	$0.0659234\pi$
$318$		0			0
$319$	−8.79293	−	2.08396i	−0.492310	−	0.116680i
$320$	−4.99907	+	0.584307i	−0.279456	+	0.0326638i
$321$		0			0
$322$	−0.384246	−	6.59724i	−0.0214132	−	0.367650i
$323$	10.0493			0.559156
$324$		0			0
$325$	−16.1482			−0.895740
$326$	0.598835	+	10.2816i	0.0331664	+	0.569445i
$327$		0			0
$328$	15.8327	−	1.85058i	0.874214	−	0.102181i
$329$	−3.83572	−	0.909083i	−0.211470	−	0.0501194i
$330$		0			0
$331$	−2.20579	+	2.96289i	−0.121241	+	0.162855i	−0.858600	−	0.512646i	$-0.828665\pi$
$331$	−2.20579	+	2.96289i	−0.121241	+	0.162855i	0.737359	+	0.675501i	$0.236073\pi$
$332$	−1.08293	−	6.14162i	−0.0594337	−	0.337065i
$333$		0			0
$334$	0.551633	−	3.12847i	0.0301840	−	0.171182i
$335$	0.687091	+	0.728274i	0.0375398	+	0.0397898i
$336$		0			0
$337$	16.4827	−	8.27793i	0.897870	−	0.450927i	0.0608800	−	0.998145i	$-0.480609\pi$
$337$	16.4827	−	8.27793i	0.897870	−	0.450927i	0.836990	+	0.547218i	$0.184313\pi$
$338$	5.39211	+	3.54644i	0.293292	+	0.192901i
$339$		0			0
$340$	−5.77819	+	1.36946i	−0.313366	+	0.0742692i
$341$	15.2298	−	5.54319i	0.824740	−	0.300181i
$342$		0			0
$343$	−15.1621	−	5.51854i	−0.818675	−	0.297973i
$344$	13.8278	+	1.61623i	0.745543	+	0.0871415i
$345$		0			0
$346$	13.7596	−	14.5844i	0.739723	−	0.784061i
$347$	20.0622	+	26.9481i	1.07699	+	1.44665i	0.885196	+	0.465218i	$0.154024\pi$
$347$	20.0622	+	26.9481i	1.07699	+	1.44665i	0.191796	+	0.981435i	$0.438569\pi$
$348$		0			0
$349$	−29.4341	−	14.7824i	−1.57557	−	0.791282i	−0.575916	−	0.817509i	$-0.695354\pi$
$349$	−29.4341	−	14.7824i	−1.57557	−	0.791282i	−0.999656	+	0.0262270i	$0.991651\pi$
$350$	1.94157	+	3.36289i	0.103781	+	0.179754i
$351$		0			0
$352$	−6.27342	+	10.8659i	−0.334374	+	0.579154i
$353$	11.1466	−	7.33122i	0.593273	−	0.390202i	−0.217072	−	0.976156i	$-0.569650\pi$
$353$	11.1466	−	7.33122i	0.593273	−	0.390202i	0.810344	+	0.585954i	$0.199280\pi$
$354$		0			0
$355$	−3.46415	+	8.03081i	−0.183858	+	0.426231i
$356$	−1.24821	−	4.16933i	−0.0661552	−	0.220974i
$357$		0			0
$358$	−2.09155	−	4.84877i	−0.110542	−	0.256265i
$359$	−6.91454	+	5.80199i	−0.364936	+	0.306217i	−0.806754	−	0.590887i	$-0.798778\pi$
$359$	−6.91454	+	5.80199i	−0.364936	+	0.306217i	0.441819	+	0.897104i	$0.354333\pi$
$360$		0			0
$361$	−9.11037	−	7.64450i	−0.479493	−	0.402342i
$362$	1.47973	−	4.94265i	0.0777730	−	0.259780i
$363$		0			0
$364$	−0.454840	+	7.80931i	−0.0238401	+	0.409319i
$365$	0.569483	−	9.77765i	0.0298081	−	0.511786i
$366$		0			0
$367$	−7.34329	+	24.5283i	−0.383316	+	1.28037i	0.521019	+	0.853545i	$0.325552\pi$
$367$	−7.34329	+	24.5283i	−0.383316	+	1.28037i	−0.904336	+	0.426821i	$0.859633\pi$
$368$	1.46997	+	1.23345i	0.0766274	+	0.0642980i
$369$		0			0
$370$	−7.51364	+	6.30469i	−0.390616	+	0.327765i
$371$	6.48908	+	15.0434i	0.336896	+	0.781013i
$372$		0			0
$373$	6.27172	+	20.9490i	0.324737	+	1.08470i	0.952053	+	0.305933i	$0.0989685\pi$
$373$	6.27172	+	20.9490i	0.324737	+	1.08470i	−0.627315	+	0.778765i	$0.715846\pi$
$374$	2.70304	−	6.26635i	0.139771	−	0.324025i
$375$		0			0
$376$	−6.89811	+	4.53696i	−0.355743	+	0.233976i
$377$	−9.46934	+	16.4014i	−0.487696	+	0.844714i
$378$		0			0
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	0.698448	−	0.715661i	$-0.253874\pi$
$379$	−5.26717	−	9.12300i	−0.270556	−	0.468617i	−0.969004	+	0.247043i	$0.920541\pi$
$380$	−3.75306	−	1.88486i	−0.192528	−	0.0966913i
$381$		0			0
$382$	3.35904	+	4.51198i	0.171864	+	0.230853i
$383$	15.0071	−	15.9066i	0.766829	−	0.812791i	−0.219839	−	0.975536i	$-0.570553\pi$
$383$	15.0071	−	15.9066i	0.766829	−	0.812791i	0.986668	+	0.162745i	$0.0520348\pi$
$384$		0			0
$385$	−3.42359	−	0.400161i	−0.174482	−	0.0203941i
$386$	−12.4552	−	4.53331i	−0.633952	−	0.230740i
$387$		0			0
$388$	1.67315	−	0.608977i	0.0849414	−	0.0309161i
$389$	−23.7332	+	5.62487i	−1.20332	+	0.285192i	−0.782906	−	0.622140i	$-0.786263\pi$
$389$	−23.7332	+	5.62487i	−1.20332	+	0.285192i	−0.420414	+	0.907332i	$0.638115\pi$
$390$		0			0
$391$	−19.0011	−	12.4972i	−0.960927	−	0.632012i
$392$	−12.9725	+	6.51502i	−0.655208	+	0.329058i
$393$		0			0
$394$	6.62672	+	7.02392i	0.333850	+	0.353860i
$395$	−2.40854	+	13.6595i	−0.121187	+	0.687285i
$396$		0			0
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	0.890775	+	0.454445i	$0.150163\pi$
$397$	4.16728	+	23.6338i	0.209150	+	1.18615i	−0.681625	+	0.731702i	$0.738726\pi$
$398$	−2.13890	+	2.87304i	−0.107214	+	0.144013i
$399$		0			0
$400$	−1.09716	−	0.260033i	−0.0548582	−	0.0130016i
$401$	−36.6641	+	4.28542i	−1.83092	+	0.214004i	−0.960495	−	0.278297i	$-0.910230\pi$
$401$	−36.6641	+	4.28542i	−1.83092	+	0.214004i	−0.870425	+	0.492301i	$0.836156\pi$
$402$		0			0
$403$	−1.97501	−	33.9095i	−0.0983820	−	1.68915i
$404$	3.02339			0.150419
$405$		0			0
$406$	4.55416			0.226019
$407$	1.23364	+	21.1808i	0.0611493	+	1.04989i
$408$		0			0
$409$	2.83591	−	0.331470i	0.140227	−	0.0163901i	−0.0456900	−	0.998956i	$-0.514549\pi$
$409$	2.83591	−	0.331470i	0.140227	−	0.0163901i	0.185917	+	0.982566i	$0.440475\pi$
$410$	5.65877	+	1.34115i	0.279467	+	0.0662348i
$411$		0			0
$412$	−3.54840	+	4.76632i	−0.174817	+	0.234820i
$413$	−2.49058	−	14.1248i	−0.122553	−	0.695035i
$414$		0			0
$415$	1.00007	−	5.67169i	0.0490916	−	0.278412i
$416$	18.0451	+	19.1267i	0.884736	+	0.937765i
$417$		0			0
$418$	4.31317	−	2.16616i	0.210964	−	0.105950i
$419$	28.7197	+	18.8893i	1.40305	+	0.922801i	0.999971	+	0.00763598i	$0.00243063\pi$
$419$	28.7197	+	18.8893i	1.40305	+	0.922801i	0.403080	+	0.915165i	$0.367940\pi$
$420$		0			0
$421$	6.08312	−	1.44172i	0.296473	−	0.0702654i	−0.0796876	−	0.996820i	$-0.525392\pi$
$421$	6.08312	−	1.44172i	0.296473	−	0.0702654i	0.376161	+	0.926555i	$0.377244\pi$
$422$	11.1790	−	4.06883i	0.544186	−	0.198067i
$423$		0			0
$424$	32.2449	+	11.7362i	1.56595	+	0.569960i
$425$	13.2732	+	1.55142i	0.643846	+	0.0752548i
$426$		0			0
$427$	10.6414	−	11.2792i	0.514972	−	0.545838i
$428$	−9.58807	−	12.8790i	−0.463457	−	0.622531i
$429$		0			0
$430$	4.53885	+	2.27949i	0.218883	+	0.109927i
$431$	1.50862	+	2.61301i	0.0726679	+	0.125864i	0.900070	−	0.435746i	$-0.143515\pi$
$431$	1.50862	+	2.61301i	0.0726679	+	0.125864i	−0.827402	+	0.561610i	$0.810182\pi$
$432$		0			0
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	0.214759	+	0.976667i	$0.431104\pi$
$433$	−15.3659	+	26.6146i	−0.738439	+	1.27901i	−0.953198	+	0.302347i	$0.902230\pi$
$434$	−6.82427	+	4.48839i	−0.327575	+	0.215450i
$435$		0			0
$436$	4.60750	−	10.6814i	0.220659	−	0.511546i
$437$	−4.61308	−	15.4087i	−0.220673	−	0.737100i
$438$		0			0
$439$	0.181258	+	0.420203i	0.00865097	+	0.0200552i	0.922487	−	0.386029i	$-0.126153\pi$
$439$	0.181258	+	0.420203i	0.00865097	+	0.0200552i	−0.913836	+	0.406084i	$0.866894\pi$
$440$	−5.53042	+	4.64057i	−0.263652	+	0.221231i
$441$		0			0
$442$	−10.9565	−	9.19361i	−0.521148	−	0.437296i
$443$	−10.0119	+	33.4420i	−0.475679	+	1.58888i	0.297520	+	0.954716i	$0.403841\pi$
$443$	−10.0119	+	33.4420i	−0.475679	+	1.58888i	−0.773199	+	0.634163i	$0.781345\pi$
$444$		0			0
$445$	0.233693	−	4.01235i	0.0110781	−	0.190204i
$446$	−0.977921	+	16.7903i	−0.0463059	+	0.795042i
$447$		0			0
$448$	1.57365	−	5.25635i	0.0743479	−	0.248339i
$449$	5.48196	+	4.59991i	0.258710	+	0.217083i	0.762912	−	0.646502i	$-0.223769\pi$
$449$	5.48196	+	4.59991i	0.258710	+	0.217083i	−0.504202	+	0.863586i	$0.668213\pi$
$450$		0			0
$451$	9.63661	−	8.08607i	0.453770	−	0.380758i
$452$	−8.99650	−	20.8562i	−0.423160	−	0.980995i
$453$		0			0
$454$	−0.650658	−	2.17335i	−0.0305369	−	0.102000i
$455$	−2.86128	+	6.63319i	−0.134139	+	0.310969i
$456$		0			0
$457$	10.5960	−	6.96910i	0.495660	−	0.326001i	−0.276947	−	0.960885i	$-0.589323\pi$
$457$	10.5960	−	6.96910i	0.495660	−	0.326001i	0.772607	+	0.634884i	$0.218952\pi$
$458$	0.635820	−	1.10127i	0.0297099	−	0.0514591i
$459$		0			0
$460$	4.75227	+	8.23117i	0.221576	+	0.383780i
$461$	−0.412693	−	0.207262i	−0.0192210	−	0.00965317i	0.439163	−	0.898408i	$-0.355275\pi$
$461$	−0.412693	−	0.207262i	−0.0192210	−	0.00965317i	−0.458384	+	0.888754i	$0.651571\pi$
$462$		0			0
$463$	22.1551	+	29.7595i	1.02964	+	1.38304i	0.921267	+	0.388931i	$0.127156\pi$
$463$	22.1551	+	29.7595i	1.02964	+	1.38304i	0.108369	+	0.994111i	$0.465437\pi$
$464$	−0.907489	+	0.961882i	−0.0421291	+	0.0446543i
$465$		0			0
$466$	5.40065	+	0.631245i	0.250180	+	0.0292419i
$467$	25.8480	+	9.40792i	1.19611	+	0.435347i	0.861863	−	0.507141i	$-0.169298\pi$
$467$	25.8480	+	9.40792i	1.19611	+	0.435347i	0.334242	+	0.942487i	$0.391520\pi$
$468$		0			0
$469$	−1.02568	+	0.373316i	−0.0473614	+	0.0172381i
$470$	−2.93096	+	0.694651i	−0.135195	+	0.0320419i
$471$		0			0
$472$	−25.0984	−	16.5075i	−1.15525	−	0.759817i
$473$	9.81808	−	4.93082i	0.451436	−	0.226720i
$474$		0			0
$475$	6.48587	+	6.87462i	0.297592	+	0.315429i
$476$	1.12413	−	6.37527i	0.0515245	−	0.292210i
$477$		0			0
$478$	−2.44425	−	13.8620i	−0.111798	−	0.634035i
$479$	8.51578	−	11.4387i	0.389096	−	0.522646i	−0.563813	−	0.825902i	$-0.690666\pi$
$479$	8.51578	−	11.4387i	0.389096	−	0.522646i	0.952909	+	0.303256i	$0.0980737\pi$
$480$		0			0
$481$	43.2672	+	10.2545i	1.97282	+	0.467566i
$482$	−10.4241	+	1.21840i	−0.474805	+	0.0554967i
$483$		0			0
$484$	−0.476647	−	8.18372i	−0.0216658	−	0.371987i
$485$	1.64429			0.0746634
$486$		0			0
$487$	9.07752			0.411342			0.205671	−	0.978621i	$-0.434062\pi$
$487$	9.07752			0.411342			0.205671	+	0.978621i	$0.434062\pi$
$488$	−1.88846	−	32.4235i	−0.0854864	−	1.46774i
$489$		0			0
$490$	−5.26023	+	0.614833i	−0.237633	+	0.0277753i
$491$	27.1313	+	6.43024i	1.22442	+	0.290193i	0.791460	−	0.611220i	$-0.209321\pi$
$491$	27.1313	+	6.43024i	1.22442	+	0.290193i	0.432960	+	0.901413i	$0.357469\pi$
$492$		0			0
$493$	9.35920	−	12.5716i	0.421517	−	0.566196i
$494$	−1.75653	−	9.96180i	−0.0790302	−	0.448203i
$495$		0			0
$496$	0.411853	−	2.33573i	0.0184927	−	0.104878i
$497$	−6.54304	−	6.93522i	−0.293495	−	0.311087i
$498$		0			0
$499$	−21.2606	+	10.6775i	−0.951755	+	0.477989i	−0.855749	−	0.517392i	$-0.826903\pi$
$499$	−21.2606	+	10.6775i	−0.951755	+	0.477989i	−0.0960058	+	0.995381i	$0.530607\pi$
$500$	−11.2470	−	7.39729i	−0.502982	−	0.330817i
$501$		0			0
$502$	−20.9143	+	4.95677i	−0.933450	+	0.221232i
$503$	−7.57016	+	2.75531i	−0.337537	+	0.122853i	−0.505227	−	0.862986i	$-0.668591\pi$
$503$	−7.57016	+	2.75531i	−0.337537	+	0.122853i	0.167690	+	0.985840i	$0.446369\pi$
$504$		0			0
$505$	2.62367	+	0.954939i	0.116752	+	0.0424942i
$506$	−10.8491	−	1.26808i	−0.482303	−	0.0563732i
$507$		0			0
$508$	5.09260	−	5.39784i	0.225948	−	0.239491i
$509$	11.5280	+	15.4848i	0.510971	+	0.686353i	0.980490	−	0.196569i	$-0.0629801\pi$
$509$	11.5280	+	15.4848i	0.510971	+	0.686353i	−0.469519	+	0.882922i	$0.655573\pi$
$510$		0			0
$511$	9.54151	+	4.79193i	0.422092	+	0.211982i
$512$	1.79397	+	3.10725i	0.0792832	+	0.137323i
$513$		0			0
$514$	−6.02780	+	10.4405i	−0.265875	+	0.460509i
$515$	−4.58471	+	3.01541i	−0.202027	+	0.132875i
$516$		0			0
$517$	−2.58072	+	5.98279i	−0.113500	+	0.263123i
$518$	−3.06668	−	10.2434i	−0.134742	−	0.450071i
$519$		0			0
$520$	5.99288	+	13.8930i	0.262805	+	0.609251i
$521$	−2.04454	+	1.71557i	−0.0895727	+	0.0751604i	−0.686474	−	0.727154i	$-0.740843\pi$
$521$	−2.04454	+	1.71557i	−0.0895727	+	0.0751604i	0.596902	+	0.802314i	$0.296398\pi$
$522$		0			0
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	0.862757	−	0.505619i	$-0.168736\pi$
$523$	11.7693	+	9.87562i	0.514636	+	0.431831i	−0.348121	+	0.937450i	$0.613180\pi$
$524$	7.31144	−	24.4219i	0.319402	−	1.06688i
$525$		0			0
$526$	0.506373	−	8.69408i	0.0220789	−	0.379080i
$527$	−1.63444	+	28.0622i	−0.0711971	+	1.22241i
$528$		0			0
$529$	−3.84339	+	12.8378i	−0.167104	+	0.558166i
$530$	9.58997	+	8.04694i	0.416562	+	0.349537i
$531$		0			0
$532$	3.50727	−	2.94295i	0.152059	−	0.127593i
$533$	−10.4424	−	24.2083i	−0.452312	−	1.04858i
$534$		0			0
$535$	−4.25260	−	14.2047i	−0.183856	−	0.614122i
$536$	−0.905489	+	2.09916i	−0.0391112	+	0.0906699i
$537$		0			0
$538$	0.146675	−	0.0964694i	0.00632359	−	0.00415909i
$539$	−5.72799	+	9.92117i	−0.246722	+	0.427335i
$540$		0			0
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	0.994191	−	0.107626i	$-0.0343250\pi$
$541$	9.39421	+	16.2713i	0.403889	+	0.699556i	−0.590303	+	0.807182i	$0.700992\pi$
$542$	8.49884	+	4.26828i	0.365057	+	0.183338i
$543$		0			0
$544$	−12.9949	−	17.4552i	−0.557151	−	0.748384i
$545$	7.37206	−	7.81393i	0.315785	−	0.334712i
$546$		0			0
$547$	11.3834	+	1.33052i	0.486717	+	0.0568891i	0.355913	−	0.934519i	$-0.384170\pi$
$547$	11.3834	+	1.33052i	0.486717	+	0.0568891i	0.130804	+	0.991408i	$0.458244\pi$
$548$	−19.4583	−	7.08223i	−0.831216	−	0.302538i
$549$		0			0
$550$	6.03132	−	2.19522i	0.257176	−	0.0936045i
$551$	10.7857	−	2.55627i	0.459488	−	0.108901i
$552$		0			0
$553$	−12.6332	−	8.30896i	−0.537217	−	0.353333i
$554$	8.29972	−	4.16828i	0.352621	−	0.177093i
$555$		0			0
$556$	−9.35662	−	9.91744i	−0.396809	−	0.420593i
$557$	−4.33665	+	24.5943i	−0.183750	+	1.04210i	0.743802	+	0.668400i	$0.233021\pi$
$557$	−4.33665	+	24.5943i	−0.183750	+	1.04210i	−0.927551	+	0.373695i	$0.878091\pi$
$558$		0			0
$559$	−3.99840	−	22.6761i	−0.169114	−	0.959095i
$560$	−0.301219	+	0.404607i	−0.0127288	+	0.0170978i
$561$		0			0
$562$	−17.5917	−	4.16930i	−0.742060	−	0.175871i
$563$	−17.4623	+	2.04106i	−0.735950	+	0.0860202i	−0.475807	−	0.879550i	$-0.657844\pi$
$563$	−17.4623	+	2.04106i	−0.735950	+	0.0860202i	−0.260143	+	0.965570i	$0.583770\pi$
$564$		0			0
$565$	−1.21964	−	20.9404i	−0.0513106	−	0.880970i
$566$	0.247007			0.0103825
$567$		0			0
$568$	−19.9700			−0.837922
$569$	0.929683	+	15.9620i	0.0389743	+	0.669164i	0.960058	+	0.279800i	$0.0902681\pi$
$569$	0.929683	+	15.9620i	0.0389743	+	0.669164i	−0.921084	+	0.389364i	$0.872695\pi$
$570$		0			0
$571$	−10.2603	+	1.19926i	−0.429380	+	0.0501873i	−0.328038	−	0.944664i	$-0.606388\pi$
$571$	−10.2603	+	1.19926i	−0.429380	+	0.0501873i	−0.101341	+	0.994852i	$0.532313\pi$
$572$	12.5813	+	2.98182i	0.526050	+	0.124676i
$573$		0			0
$574$	−3.78588	+	5.08532i	−0.158020	+	0.212257i
$575$	−3.71420	−	21.0643i	−0.154893	−	0.878441i
$576$		0			0
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	−0.429351	−	0.903138i	$-0.641258\pi$
$577$	6.79785	−	38.5525i	0.282998	−	1.60496i	0.712349	−	0.701825i	$-0.247631\pi$
$578$	−1.59541	−	1.69104i	−0.0663604	−	0.0703379i
$579$		0			0
$580$	−5.85330	+	2.93964i	−0.243045	+	0.122062i
$581$	5.24553	+	3.45004i	0.217621	+	0.143132i
$582$		0			0
$583$	26.3498	−	6.24502i	1.09130	−	0.258642i
$584$	21.0145	−	7.64866i	0.869587	−	0.316504i
$585$		0			0
$586$	11.3554	+	4.13304i	0.469088	+	0.170734i
$587$	−17.6814	−	2.06665i	−0.729788	−	0.0853000i	−0.256919	−	0.966433i	$-0.582707\pi$
$587$	−17.6814	−	2.06665i	−0.729788	−	0.0853000i	−0.472869	+	0.881133i	$0.656782\pi$
$588$		0			0
$589$	−13.6427	+	14.4605i	−0.562139	+	0.595833i
$590$	−6.54460	−	8.79092i	−0.269437	−	0.361916i
$591$		0			0
$592$	2.77460	+	1.39346i	0.114035	+	0.0572707i
$593$	−6.92687	−	11.9977i	−0.284452	−	0.492686i	0.688024	−	0.725688i	$-0.258478\pi$
$593$	−6.92687	−	11.9977i	−0.284452	−	0.492686i	−0.972476	+	0.233002i	$0.925145\pi$
$594$		0			0
$595$	2.98914	−	5.17735i	0.122543	−	0.212251i
$596$	3.18104	−	2.09220i	0.130300	−	0.0856999i
$597$		0			0
$598$	−9.06720	+	21.0201i	−0.370786	+	0.859577i
$599$	1.03796	+	3.46703i	0.0424099	+	0.141659i	0.976572	−	0.215189i	$-0.0690367\pi$
$599$	1.03796	+	3.46703i	0.0424099	+	0.141659i	−0.934163	+	0.356848i	$0.883851\pi$
$600$		0			0
$601$	−4.11249	−	9.53383i	−0.167752	−	0.388893i	0.813515	−	0.581543i	$-0.197551\pi$
$601$	−4.11249	−	9.53383i	−0.167752	−	0.388893i	−0.981267	+	0.192650i	$0.938292\pi$
$602$	−4.24159	+	3.55912i	−0.172874	+	0.145059i
$603$		0			0
$604$	12.7665	+	10.7124i	0.519462	+	0.435880i
$605$	2.17120	−	7.25231i	0.0882718	−	0.294848i
$606$		0			0
$607$	−0.781051	+	13.4101i	−0.0317019	+	0.544301i	0.944645	+	0.328093i	$0.106406\pi$
$607$	−0.781051	+	13.4101i	−0.0317019	+	0.544301i	−0.976347	+	0.216208i	$0.930631\pi$
$608$	0.894873	−	15.3644i	0.0362919	−	0.623108i
$609$		0			0
$610$	3.39835	−	11.3513i	0.137595	−	0.459599i
$611$	10.4607	+	8.77758i	0.423195	+	0.355103i
$612$		0			0
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	−0.0707686	−	0.997493i	$-0.522545\pi$
$613$	22.2652	−	18.6827i	0.899281	−	0.754587i	0.970050	+	0.242906i	$0.0781007\pi$
$614$	−1.25015	−	2.89817i	−0.0504519	−	0.116961i
$615$		0			0
$616$	−2.25723	−	7.53968i	−0.0909465	−	0.303782i
$617$	−4.92341	+	11.4138i	−0.198209	+	0.459500i	−0.988113	−	0.153730i	$-0.950871\pi$
$617$	−4.92341	+	11.4138i	−0.198209	+	0.459500i	0.789904	+	0.613231i	$0.210130\pi$
$618$		0			0
$619$	−28.8790	+	18.9940i	−1.16074	+	0.763434i	−0.975660	−	0.219289i	$-0.929626\pi$
$619$	−28.8790	+	18.9940i	−1.16074	+	0.763434i	−0.185085	+	0.982723i	$0.559256\pi$
$620$	5.87380	−	10.1737i	0.235898	−	0.408586i
$621$		0			0
$622$	−5.13533	−	8.89464i	−0.205908	−	0.356643i
$623$	3.91545	+	1.96641i	0.156869	+	0.0787827i
$624$		0			0
$625$	3.16157	+	4.24673i	0.126463	+	0.169869i
$626$	3.89053	−	4.12373i	0.155497	−	0.164817i
$627$		0			0
$628$	−1.64834	−	0.192664i	−0.0657761	−	0.00768812i
$629$	−34.5789	−	12.5857i	−1.37875	−	0.501825i
$630$		0			0
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	−0.0826292	−	0.996580i	$-0.526332\pi$
$631$	12.4258	−	4.52262i	0.494663	−	0.180042i	0.577292	+	0.816538i	$0.304109\pi$
$632$	−30.8163	+	7.30359i	−1.22581	+	0.290521i
$633$		0			0
$634$	10.3954	+	6.83716i	0.412854	+	0.271538i
$635$	6.12422	−	3.07570i	0.243032	−	0.122055i
$636$		0			0
$637$	16.4762	+	17.4638i	0.652813	+	0.691941i
$638$	1.30714	−	7.41317i	0.0517502	−	0.293490i
$639$		0			0
$640$	1.69021	+	9.58567i	0.0668115	+	0.378907i
$641$	3.14875	−	4.22950i	0.124368	−	0.167055i	−0.735578	−	0.677440i	$-0.763089\pi$
$641$	3.14875	−	4.22950i	0.124368	−	0.167055i	0.859946	+	0.510384i	$0.170497\pi$
$642$		0			0
$643$	4.25864	+	1.00932i	0.167944	+	0.0398035i	0.313728	−	0.949513i	$-0.398422\pi$
$643$	4.25864	+	1.00932i	0.167944	+	0.0398035i	−0.145783	+	0.989317i	$0.546570\pi$
$644$	−10.2914	+	1.20289i	−0.405537	+	0.0474004i
$645$		0			0
$646$	0.486740	+	8.35700i	0.0191505	+	0.328802i
$647$	−5.42624			−0.213327			−0.106664	−	0.994295i	$-0.534017\pi$
$647$	−5.42624			−0.213327			−0.106664	+	0.994295i	$0.534017\pi$
$648$		0			0
$649$	−23.7069			−0.930576
$650$	−0.782143	−	13.4289i	−0.0306782	−	0.526724i
$651$		0			0
$652$	16.0388	−	1.87466i	0.628127	−	0.0734175i
$653$	−10.8018	−	2.56007i	−0.422706	−	0.100183i	0.0137571	−	0.999905i	$-0.495621\pi$
$653$	−10.8018	−	2.56007i	−0.422706	−	0.100183i	−0.436463	+	0.899722i	$0.643769\pi$
$654$		0			0
$655$	14.0585	−	18.8838i	0.549310	−	0.737851i
$656$	−0.319672	−	1.81295i	−0.0124811	−	0.0707837i
$657$		0			0
$658$	0.570212	−	3.23383i	0.0222292	−	0.126068i
$659$	−5.10241	−	5.40824i	−0.198762	−	0.210675i	0.620325	−	0.784345i	$-0.287001\pi$
$659$	−5.10241	−	5.40824i	−0.198762	−	0.210675i	−0.819087	+	0.573670i	$0.805519\pi$
$660$		0			0
$661$	−3.42406	+	1.71963i	−0.133180	+	0.0668858i	−0.514142	−	0.857705i	$-0.671889\pi$
$661$	−3.42406	+	1.71963i	−0.133180	+	0.0668858i	0.380961	+	0.924591i	$0.375593\pi$
$662$	−2.57079	−	1.69083i	−0.0999165	−	0.0657161i
$663$		0			0
$664$	12.7955	−	3.03259i	0.496562	−	0.117687i
$665$	3.97311	−	1.44609i	0.154071	−	0.0560771i
$666$		0			0
$667$	−23.5726	−	8.57971i	−0.912733	−	0.332208i
$668$	−4.94716	−	0.578240i	−0.191411	−	0.0223728i
$669$		0			0
$670$	−0.572355	+	0.606661i	−0.0221120	+	0.0234374i
$671$	−15.3057	−	20.5592i	−0.590871	−	0.793678i
$672$		0			0
$673$	37.6141	+	18.8905i	1.44992	+	0.728177i	0.987372	−	0.158418i	$-0.0506395\pi$
$673$	37.6141	+	18.8905i	1.44992	+	0.728177i	0.462547	+	0.886595i	$0.346936\pi$
$674$	7.68230	+	13.3061i	0.295911	+	0.512533i
$675$		0			0
$676$	5.05953	−	8.76336i	0.194597	−	0.337052i
$677$	−2.08236	+	1.36959i	−0.0800315	+	0.0526376i	−0.588894	−	0.808210i	$-0.700437\pi$
$677$	−2.08236	+	1.36959i	−0.0800315	+	0.0526376i	0.508863	+	0.860848i	$0.330066\pi$
$678$		0			0
$679$	−0.709986	+	1.64593i	−0.0272468	+	0.0631651i
$680$	−3.59117	−	11.9953i	−0.137715	−	0.460001i
$681$		0			0
$682$	5.34740	+	12.3967i	0.204762	+	0.474693i
$683$	11.7411	−	9.85194i	0.449260	−	0.376974i	−0.389901	−	0.920857i	$-0.627491\pi$
$683$	11.7411	−	9.85194i	0.449260	−	0.376974i	0.839161	+	0.543883i	$0.183046\pi$
$684$		0			0
$685$	−14.6488	−	12.2918i	−0.559701	−	0.469645i
$686$	3.85486	−	12.8761i	0.147179	−	0.491613i
$687$		0			0
$688$	0.0934850	−	1.60508i	0.00356408	−	0.0611930i
$689$	3.29993	−	56.6575i	0.125717	−	2.15848i
$690$		0			0
$691$	−10.6430	+	35.5501i	−0.404879	+	1.35239i	0.476165	+	0.879356i	$0.342027\pi$
$691$	−10.6430	+	35.5501i	−0.404879	+	1.35239i	−0.881044	+	0.473035i	$0.843159\pi$
$692$	−24.0827	−	20.2078i	−0.915488	−	0.768186i
$693$		0			0
$694$	−21.4384	+	17.9890i	−0.813792	+	0.682853i
$695$	−4.98717	−	11.5616i	−0.189174	−	0.438555i
$696$		0			0
$697$	6.25752	+	20.9016i	0.237021	+	0.791704i
$698$	10.8674	−	25.1935i	0.411338	−	0.953588i
$699$		0			0
$700$	5.08679	−	3.34564i	0.192263	−	0.126453i
$701$	3.35489	−	5.81083i	0.126712	−	0.219472i	−0.795689	−	0.605706i	$-0.792891\pi$
$701$	3.35489	−	5.81083i	0.126712	−	0.219472i	0.922401	+	0.386234i	$0.126224\pi$
$702$		0			0
$703$	−13.0126	−	22.5385i	−0.490779	−	0.850054i
$704$	−8.10452	−	4.07024i	−0.305450	−	0.153403i
$705$		0			0
$706$	6.63656	+	8.91444i	0.249770	+	0.335499i
$707$	−2.08876	+	2.21396i	−0.0785560	+	0.0832645i
$708$		0			0
$709$	23.6203	+	2.76081i	0.887078	+	0.103685i	0.547413	−	0.836862i	$-0.315613\pi$
$709$	23.6203	+	2.76081i	0.887078	+	0.103685i	0.339664	+	0.940547i	$0.389687\pi$
$710$	−6.84623	−	2.49182i	−0.256934	−	0.0935165i
$711$		0			0
$712$	8.62351	−	3.13870i	0.323180	−	0.117628i
$713$	43.7786	−	10.3757i	1.63952	−	0.388573i
$714$		0			0
$715$	9.97612	+	6.56140i	0.373086	+	0.245382i
$716$	−7.39890	+	3.71587i	−0.276510	+	0.138868i
$717$		0			0
$718$	−5.15986	−	5.46913i	−0.192564	−	0.204106i
$719$	7.41202	−	42.0356i	0.276422	−	1.56766i	−0.457988	−	0.888958i	$-0.651430\pi$
$719$	7.41202	−	42.0356i	0.276422	−	1.56766i	0.734410	−	0.678706i	$-0.237459\pi$
$720$		0			0
$721$	−1.03880	−	5.89131i	−0.0386868	−	0.219404i
$722$	5.91593	−	7.94647i	0.220168	−	0.295737i
$723$		0			0
$724$	−7.87144	−	1.86556i	−0.292540	−	0.0693332i
$725$	14.6406	−	1.71124i	0.543739	−	0.0635539i
$726$		0			0
$727$	−1.10799	−	19.0235i	−0.0410932	−	0.705544i	−0.954448	−	0.298378i	$-0.903554\pi$
$727$	−1.10799	−	19.0235i	−0.0410932	−	0.705544i	0.913354	−	0.407165i	$-0.133483\pi$
$728$	−16.4946			−0.611329
$729$		0			0
$730$	8.15871			0.301967
$731$	1.10797	+	19.0231i	0.0409796	+	0.703593i
$732$		0			0
$733$	17.8418	−	2.08541i	0.659001	−	0.0770262i	0.219982	−	0.975504i	$-0.429400\pi$
$733$	17.8418	−	2.08541i	0.659001	−	0.0770262i	0.439019	+	0.898478i	$0.355326\pi$
$734$	−20.7535	−	4.91866i	−0.766025	−	0.181551i
$735$		0			0
$736$	−20.7991	+	27.9380i	−0.766665	+	1.02981i
$737$	0.313285	+	1.77673i	0.0115400	+	0.0654466i
$738$		0			0
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	−0.918700	−	0.394955i	$-0.870760\pi$
$739$	2.16602	−	12.2841i	0.0796782	−	0.451878i	0.998379	−	0.0569224i	$-0.0181288\pi$
$740$	10.5535	+	11.1860i	0.387953	+	0.411206i
$741$		0			0
$742$	−12.1958	+	6.12497i	−0.447722	+	0.224855i
$743$	−21.6533	−	14.2416i	−0.794384	−	0.522474i	0.0862493	−	0.996274i	$-0.472512\pi$
$743$	−21.6533	−	14.2416i	−0.794384	−	0.522474i	−0.880633	+	0.473799i	$0.842882\pi$
$744$		0			0
$745$	3.42130	−	0.810863i	0.125347	−	0.0297077i
$746$	−17.1175	+	6.23026i	−0.626716	+	0.228106i
$747$		0			0
$748$	−10.0549	−	3.65968i	−0.367643	−	0.133811i
$749$	16.0551	+	1.87657i	0.586640	+	0.0685684i
$750$		0			0
$751$	−7.20276	+	7.63448i	−0.262832	+	0.278586i	−0.845328	−	0.534248i	$-0.820595\pi$
$751$	−7.20276	+	7.63448i	−0.262832	+	0.278586i	0.582495	+	0.812834i	$0.302076\pi$
$752$	0.569393	+	0.764827i	0.0207636	+	0.0278904i
$753$		0			0
$754$	−14.0981	−	7.08032i	−0.513422	−	0.257850i
$755$	7.69516	+	13.3284i	0.280056	+	0.485070i
$756$		0			0
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	−0.867592	−	0.497277i	$-0.834333\pi$
$757$	−0.0864170	+	0.149679i	−0.00314088	+	0.00544016i	0.864451	+	0.502718i	$0.167666\pi$
$758$	7.33160	−	4.82207i	0.266296	−	0.175145i
$759$		0			0
$760$	3.50754	−	8.13139i	0.127232	−	0.294957i
$761$	0.537224	+	1.79445i	0.0194743	+	0.0650488i	0.967174	−	0.254113i	$-0.0817837\pi$
$761$	0.537224	+	1.79445i	0.0194743	+	0.0650488i	−0.947700	+	0.319162i	$0.896598\pi$
$762$		0			0
$763$	4.63856	+	10.7534i	0.167927	+	0.389299i
$764$	6.75618	−	5.66911i	0.244430	−	0.205101i
$765$		0			0
$766$	13.9549	+	11.7095i	0.504211	+	0.423083i
$767$	−14.2497	+	47.5974i	−0.514528	+	1.71864i
$768$		0			0
$769$	1.62282	−	27.8628i	0.0585204	−	1.00476i	−0.833430	−	0.552624i	$-0.813626\pi$
$769$	1.62282	−	27.8628i	0.0585204	−	1.00476i	0.891951	−	0.452132i	$-0.149337\pi$
$770$	0.166952	−	2.86645i	0.00601653	−	0.103300i
$771$		0			0
$772$	−5.96032	+	19.9089i	−0.214517	+	0.716536i
$773$	−0.0418155	−	0.0350873i	−0.00150400	−	0.00126200i	0.642035	−	0.766675i	$-0.278090\pi$
$773$	−0.0418155	−	0.0350873i	−0.00150400	−	0.00126200i	−0.643539	+	0.765413i	$0.722535\pi$
$774$		0			0
$775$	−20.2520	+	16.9934i	−0.727472	+	0.610422i
$776$	1.48705	+	3.44737i	0.0533819	+	0.123753i
$777$		0			0
$778$	−5.82718	−	19.4641i	−0.208915	−	0.697823i
$779$	−6.11180	+	14.1687i	−0.218978	+	0.507648i
$780$		0			0
$781$	−13.1670	+	8.66007i	−0.471152	+	0.309882i
$782$	9.47240	−	16.4067i	0.338732	−	0.586702i
$783$		0			0
$784$	0.838235	+	1.45187i	0.0299370	+	0.0518524i
$785$	−1.36957	−	0.687821i	−0.0488819	−	0.0245494i
$786$		0			0
$787$	−20.2554	−	27.2077i	−0.722025	−	0.969848i	−0.999957	−	0.00924767i	$-0.997056\pi$
$787$	−20.2554	−	27.2077i	−0.722025	−	0.969848i	0.277932	−	0.960601i	$-0.410351\pi$
$788$	10.3901	−	11.0129i	0.370133	−	0.392318i
$789$		0			0
$790$	−11.4760	−	1.34135i	−0.408296	−	0.0477230i
$791$	21.4879	+	7.82097i	0.764023	+	0.278082i
$792$		0			0
$793$	−50.4776	+	18.3724i	−1.79251	+	0.652422i
$794$	−19.4521	+	4.61023i	−0.690330	+	0.163611i
$795$		0			0
$796$	4.69206	+	3.08601i	0.166306	+	0.109381i
$797$	−13.0138	+	6.53577i	−0.460972	+	0.231509i	−0.664101	−	0.747643i	$-0.731185\pi$
$797$	−13.0138	+	6.53577i	−0.460972	+	0.231509i	0.203129	+	0.979152i	$0.434889\pi$
$798$		0			0
$799$	−7.75504	−	8.21986i	−0.274354	−	0.290798i
$800$	3.55394	−	20.1554i	0.125651	−	0.712600i
$801$		0			0
$802$	−5.33961	−	30.2825i	−0.188548	−	1.06931i
$803$	10.5388	−	14.1561i	0.371907	−	0.499558i
$804$		0			0
$805$	−9.31069	−	2.20667i	−0.328159	−	0.0777750i
$806$	28.1036	−	3.28484i	0.989908	−	0.115704i
$807$		0			0
$808$	0.370679	+	6.36432i	0.0130405	+	0.223896i
$809$	−28.0189			−0.985092			−0.492546	−	0.870286i	$-0.663934\pi$
$809$	−28.0189			−0.985092			−0.492546	+	0.870286i	$0.663934\pi$
$810$		0			0
$811$	29.1924			1.02508			0.512542	−	0.858662i	$-0.328704\pi$
$811$	29.1924			1.02508			0.512542	+	0.858662i	$0.328704\pi$
$812$	−0.415184	−	7.12844i	−0.0145701	−	0.250159i
$813$		0			0
$814$	−17.5543	+	2.05180i	−0.615276	+	0.0719155i
$815$	14.5104	+	3.43903i	0.508278	+	0.120464i
$816$		0			0
$817$	−8.04773	+	10.8100i	−0.281554	+	0.378193i
$818$	0.413009	+	2.34229i	0.0144405	+	0.0818964i
$819$		0			0
$820$	1.58337	−	8.97971i	0.0552935	−	0.313585i
$821$	−20.4884	−	21.7164i	−0.715049	−	0.757908i	0.263335	−	0.964704i	$-0.415178\pi$
$821$	−20.4884	−	21.7164i	−0.715049	−	0.757908i	−0.978384	+	0.206797i	$0.933696\pi$
$822$		0			0
$823$	−35.9168	+	18.0381i	−1.25198	+	0.628769i	−0.946277	−	0.323357i	$-0.895188\pi$
$823$	−35.9168	+	18.0381i	−1.25198	+	0.628769i	−0.305705	+	0.952126i	$0.598892\pi$
$824$	−10.4683	−	6.88510i	−0.364680	−	0.239854i
$825$		0			0
$826$	11.6256	−	2.75531i	0.404505	−	0.0958695i
$827$	−39.9498	+	14.5405i	−1.38919	+	0.505623i	−0.924951	−	0.380087i	$-0.875894\pi$
$827$	−39.9498	+	14.5405i	−1.38919	+	0.505623i	−0.464238	+	0.885710i	$0.653672\pi$
$828$		0			0
$829$	5.90599	+	2.14960i	0.205124	+	0.0746589i	0.442539	−	0.896749i	$-0.354078\pi$
$829$	5.90599	+	2.14960i	0.205124	+	0.0746589i	−0.237415	+	0.971408i	$0.576300\pi$
$830$	4.76503	+	0.556952i	0.165397	+	0.0193321i
$831$		0			0
$832$	−13.0435	+	13.8253i	−0.452202	+	0.479306i
$833$	−11.8651	−	15.9376i	−0.411100	−	0.552204i
$834$		0			0
$835$	−4.11046	−	2.06435i	−0.142248	−	0.0714398i
$836$	−3.78381	−	6.55375i	−0.130866	−	0.226666i
$837$		0			0
$838$	−14.3173	+	24.7983i	−0.494584	+	0.856644i
$839$	13.8375	−	9.10107i	0.477724	−	0.314204i	−0.287711	−	0.957717i	$-0.592894\pi$
$839$	13.8375	−	9.10107i	0.477724	−	0.314204i	0.765435	+	0.643513i	$0.222524\pi$
$840$		0			0
$841$	−4.63910	+	10.7546i	−0.159969	+	0.370849i
$842$	1.49358	+	4.98891i	0.0514722	+	0.171929i
$843$		0			0
$844$	−7.38791	−	17.1271i	−0.254303	−	0.589539i
$845$	7.15852	−	6.00671i	0.246261	−	0.206637i
$846$		0			0
$847$	6.32205	+	5.30483i	0.217228	+	0.182276i
$848$	1.13656	−	3.79637i	0.0390296	−	0.130368i
$849$		0			0
$850$	−0.647271	+	11.1132i	−0.0222012	+	0.381180i
$851$	−3.42459	+	58.7980i	−0.117393	+	2.01557i
$852$		0			0
$853$	14.9484	−	49.9311i	0.511823	−	1.70961i	−0.176586	−	0.984285i	$-0.556505\pi$
$853$	14.9484	−	49.9311i	0.511823	−	1.70961i	0.688409	−	0.725323i	$-0.258309\pi$
$854$	9.89523	+	8.30308i	0.338608	+	0.284126i
$855$		0			0
$856$	25.9351	−	21.7622i	0.886445	−	0.743815i
$857$	15.4005	+	35.7024i	0.526071	+	1.21957i	0.949536	+	0.313658i	$0.101555\pi$
$857$	15.4005	+	35.7024i	0.526071	+	1.21957i	−0.423465	+	0.905913i	$0.639186\pi$
$858$		0			0
$859$	6.22471	+	20.7920i	0.212384	+	0.709413i	0.996095	+	0.0882870i	$0.0281393\pi$
$859$	6.22471	+	20.7920i	0.212384	+	0.709413i	−0.783711	+	0.621126i	$0.786676\pi$
$860$	3.15421	−	7.31228i	0.107558	−	0.249347i
$861$		0			0
$862$	−2.09992	+	1.38114i	−0.0715236	+	0.0470418i
$863$	21.9404	−	38.0020i	0.746861	−	1.29360i	−0.202459	−	0.979291i	$-0.564893\pi$
$863$	21.9404	−	38.0020i	0.746861	−	1.29360i	0.949320	−	0.314311i	$-0.101773\pi$
$864$		0			0
$865$	−14.5161	−	25.1427i	−0.493564	−	0.854877i
$866$	−22.8770	−	11.4893i	−0.777392	−	0.390421i
$867$		0			0
$868$	7.64764	+	10.2726i	0.259578	+	0.348673i
$869$	−17.1512	+	18.1792i	−0.581813	+	0.616686i
$870$		0			0
$871$	3.75553	+	0.438959i	0.127251	+	0.0148736i
$872$	23.0495	+	8.38933i	0.780554	+	0.284099i
$873$		0			0
$874$	12.5905	−	4.58258i	0.425881	−	0.155008i
$875$	13.1871	−	3.12539i	0.445804	−	0.105658i
$876$		0			0
$877$	20.9882	+	13.8042i	0.708721	+	0.466133i	0.851995	−	0.523550i	$-0.175393\pi$
$877$	20.9882	+	13.8042i	0.708721	+	0.466133i	−0.143274	+	0.989683i	$0.545763\pi$
$878$	−0.340663	+	0.171087i	−0.0114968	+	0.00577392i
$879$		0			0
$880$	0.572155	+	0.606449i	0.0192873	+	0.0204434i
$881$	−0.463850	+	2.63063i	−0.0156275	+	0.0886281i	−0.991624	−	0.129158i	$-0.958772\pi$
$881$	−0.463850	+	2.63063i	−0.0156275	+	0.0886281i	0.975996	+	0.217786i	$0.0698836\pi$
$882$		0			0
$883$	6.82642	+	38.7145i	0.229727	+	1.30285i	0.853439	+	0.521193i	$0.174513\pi$
$883$	6.82642	+	38.7145i	0.229727	+	1.30285i	−0.623711	+	0.781655i	$0.714376\pi$
$884$	−13.3915	+	17.9879i	−0.450406	+	0.605000i
$885$		0			0
$886$	−28.2954	−	6.70614i	−0.950604	−	0.225297i
$887$	33.1937	−	3.87979i	1.11454	−	0.130271i	0.461169	−	0.887312i	$-0.347430\pi$
$887$	33.1937	−	3.87979i	1.11454	−	0.130271i	0.653367	+	0.757041i	$0.273356\pi$
$888$		0			0
$889$	0.434402	+	7.45839i	0.0145694	+	0.250146i
$890$	3.34800			0.112225
$891$		0			0
$892$	26.3703			0.882942
$893$	−0.464714	−	7.97883i	−0.0155511	−	0.267001i
$894$		0			0
$895$	−7.59436	+	0.887653i	−0.253851	+	0.0296710i
$896$	−10.3251	−	2.44708i	−0.344936	−	0.0817513i
$897$		0			0
$898$	−3.55978	+	4.78161i	−0.118791	+	0.159565i
$899$	5.38405	+	30.5345i	0.179568	+	1.01838i
$900$		0			0
$901$	−8.15573	+	46.2534i	−0.271707	+	1.54093i
$902$	7.19116	+	7.62218i	0.239439	+	0.253791i
$903$		0			0
$904$	42.7999	−	21.4949i	1.42350	−	0.714911i
$905$	−6.24152	−	4.10511i	−0.207475	−	0.136459i
$906$		0			0
$907$	−11.9717	+	2.83735i	−0.397515	+	0.0942127i	−0.424511	−	0.905423i	$-0.639554\pi$
$907$	−11.9717	+	2.83735i	−0.397515	+	0.0942127i	0.0269963	+	0.999636i	$0.491406\pi$
$908$	−3.34254	+	1.21658i	−0.110926	+	0.0403738i
$909$		0			0
$910$	−5.65477	−	2.05817i	−0.187454	−	0.0682276i
$911$	−21.7054	−	2.53700i	−0.719131	−	0.0840544i	−0.251347	−	0.967897i	$-0.580874\pi$
$911$	−21.7054	−	2.53700i	−0.719131	−	0.0840544i	−0.467784	+	0.883843i	$0.654948\pi$
$912$		0			0
$913$	7.12148	−	7.54833i	0.235687	−	0.249813i
$914$	6.30875	+	8.47412i	0.208675	+	0.280299i
$915$		0			0
$916$	−1.78174	−	0.894825i	−0.0588704	−	0.0295658i
$917$	12.8324	+	22.2263i	0.423762	+	0.733977i
$918$		0			0
$919$	27.9349	−	48.3846i	0.921487	−	1.59606i	0.124370	−	0.992236i	$-0.460309\pi$
$919$	27.9349	−	48.3846i	0.921487	−	1.59606i	0.797116	−	0.603826i	$-0.206358\pi$
$920$	−16.7442	+	11.0128i	−0.552040	+	0.363082i
$921$		0			0
$922$	0.152371	−	0.353236i	0.00501807	−	0.0116332i
$923$	9.47282	+	31.6414i	0.311802	+	1.04149i
$924$		0			0
$925$	−13.7077	−	31.7780i	−0.450707	−	1.04486i
$926$	−23.6750	+	19.8657i	−0.778009	+	0.652827i
$927$		0			0
$928$	−18.3873	−	15.4288i	−0.603594	−	0.506476i
$929$	12.3051	−	41.1019i	0.403718	−	1.34851i	−0.478673	−	0.877993i	$-0.658882\pi$
$929$	12.3051	−	41.1019i	0.403718	−	1.34851i	0.882391	−	0.470518i	$-0.155933\pi$
$930$		0			0
$931$	0.817071	−	14.0286i	0.0267784	−	0.459767i
$932$	0.495707	−	8.51096i	0.0162374	−	0.278786i
$933$		0			0
$934$	−6.57170	+	21.9510i	−0.215032	+	0.718258i
$935$	−7.56964	−	6.35168i	−0.247554	−	0.207722i
$936$		0			0
$937$	−10.4519	+	8.77015i	−0.341447	+	0.286508i	−0.797345	−	0.603524i	$-0.793763\pi$
$937$	−10.4519	+	8.77015i	−0.341447	+	0.286508i	0.455898	+	0.890032i	$0.349318\pi$
$938$	−0.360130	−	0.834875i	−0.0117587	−	0.0272597i
$939$		0			0
$940$	1.35451	+	4.52439i	0.0441794	+	0.147569i
$941$	−17.6077	+	40.8193i	−0.573995	+	1.33067i	0.345814	+	0.938303i	$0.387603\pi$
$941$	−17.6077	+	40.8193i	−0.573995	+	1.33067i	−0.919809	+	0.392367i	$0.871656\pi$
$942$		0			0
$943$	29.1763	−	19.1896i	0.950112	−	0.624898i
$944$	−1.73463	+	3.00447i	−0.0564575	+	0.0977873i
$945$		0			0
$946$	4.57603	+	7.92592i	0.148780	+	0.257694i
$947$	3.87411	+	1.94565i	0.125892	+	0.0632251i	0.510630	−	0.859800i	$-0.329412\pi$
$947$	3.87411	+	1.94565i	0.125892	+	0.0632251i	−0.384739	+	0.923026i	$0.625708\pi$
$948$		0			0
$949$	−22.0872	−	29.6683i	−0.716981	−	0.963073i
$950$	−5.40281	+	5.72664i	−0.175290	+	0.185797i
$951$		0			0
$952$	13.5579	+	1.58470i	0.439416	+	0.0513603i
$953$	34.6339	+	12.6057i	1.12190	+	0.408339i	0.835346	−	0.549724i	$-0.185267\pi$
$953$	34.6339	+	12.6057i	1.12190	+	0.408339i	0.286556	+	0.958063i	$0.407489\pi$
$954$		0			0
$955$	7.65355	−	2.78566i	0.247663	−	0.0901419i
$956$	−21.4749	+	5.08964i	−0.694547	+	0.164611i
$957$		0			0
$958$	9.92490	+	6.52771i	0.320659	+	0.210901i
$959$	18.6292	−	9.35595i	0.601569	−	0.302119i
$960$		0			0
$961$	−16.8879	−	17.9001i	−0.544770	−	0.577422i
$962$	−6.43203	+	36.4778i	−0.207377	+	1.17609i
$963$		0			0
$964$	2.85744	+	16.2054i	0.0920320	+	0.521939i
$965$	−11.4605	+	15.3942i	−0.368928	+	0.495556i
$966$		0			0
$967$	−9.95790	−	2.36007i	−0.320225	−	0.0758946i	0.0673601	−	0.997729i	$-0.478542\pi$
$967$	−9.95790	−	2.36007i	−0.320225	−	0.0758946i	−0.387585	+	0.921834i	$0.626691\pi$
$968$	17.1685	−	2.00671i	0.551817	−	0.0644981i
$969$		0			0
$970$	0.0796419	+	1.36740i	0.00255715	+	0.0439045i
$971$	43.9486			1.41038			0.705188	−	0.709020i	$-0.250862\pi$
$971$	43.9486			1.41038			0.705188	+	0.709020i	$0.250862\pi$
$972$		0			0
$973$	13.7265			0.440051
$974$	0.439673	+	7.54889i	0.0140880	+	0.241882i
$975$		0			0
$976$	−3.72547	+	0.435446i	−0.119250	+	0.0139383i
$977$	−57.4171	−	13.6081i	−1.83694	−	0.435362i	−0.842318	−	0.538980i	$-0.818810\pi$
$977$	−57.4171	−	13.6081i	−1.83694	−	0.435362i	−0.994617	+	0.103619i	$0.966958\pi$
$978$		0			0
$979$	4.32471	−	5.80909i	0.138218	−	0.185659i
$980$	1.44193	+	8.17758i	0.0460607	+	0.261223i
$981$		0			0
$982$	−4.03329	+	22.8740i	−0.128708	+	0.729937i
$983$	−18.3835	−	19.4854i	−0.586344	−	0.621488i	0.364483	−	0.931210i	$-0.381246\pi$
$983$	−18.3835	−	19.4854i	−0.586344	−	0.621488i	−0.950827	+	0.309722i	$0.899764\pi$
$984$		0			0
$985$	12.4949	−	6.27516i	0.398120	−	0.199943i
$986$	10.9079	+	7.17423i	0.347378	+	0.228474i
$987$		0			0
$988$	−15.4327	+	3.65761i	−0.490979	+	0.116364i
$989$	28.6598	−	10.4313i	0.911329	−	0.331697i
$990$		0			0
$991$	8.60252	+	3.13106i	0.273268	+	0.0994614i	0.475019	−	0.879975i	$-0.342441\pi$
$991$	8.60252	+	3.13106i	0.273268	+	0.0994614i	−0.201751	+	0.979437i	$0.564663\pi$
$992$	42.7589	+	4.99779i	1.35760	+	0.158680i
$993$		0			0
$994$	5.45043	−	5.77712i	0.172877	−	0.183239i
$995$	3.09701	+	4.16000i	0.0981817	+	0.131881i
$996$		0			0
$997$	37.8253	+	18.9966i	1.19794	+	0.601628i	0.932034	−	0.362370i	$-0.118032\pi$
$997$	37.8253	+	18.9966i	1.19794	+	0.601628i	0.265907	+	0.963999i	$0.414329\pi$
$998$	−9.90918	−	17.1632i	−0.313670	−	0.543292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.514.6		144
3.2	odd	2		729.2.g.d.514.3		144
9.2	odd	6		729.2.g.c.28.3		144
9.4	even	3		243.2.g.a.10.3		144
9.5	odd	6		81.2.g.a.13.6	✓	144
9.7	even	3		729.2.g.b.28.6		144
81.2	odd	54		729.2.g.d.217.3		144
81.22	even	27		6561.2.a.d.1.24		72
81.25	even	27		729.2.g.b.703.6		144
81.29	odd	54		81.2.g.a.25.6	yes	144
81.52	even	27		243.2.g.a.73.3		144
81.56	odd	54		729.2.g.c.703.3		144
81.59	odd	54		6561.2.a.c.1.49		72
81.79	even	27	inner	729.2.g.a.217.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.6	✓	144	9.5	odd	6
81.2.g.a.25.6	yes	144	81.29	odd	54
243.2.g.a.10.3		144	9.4	even	3
243.2.g.a.73.3		144	81.52	even	27
729.2.g.a.217.6		144	81.79	even	27	inner
729.2.g.a.514.6		144	1.1	even	1	trivial
729.2.g.b.28.6		144	9.7	even	3
729.2.g.b.703.6		144	81.25	even	27
729.2.g.c.28.3		144	9.2	odd	6
729.2.g.c.703.3		144	81.56	odd	54
729.2.g.d.217.3		144	81.2	odd	54
729.2.g.d.514.3		144	3.2	odd	2
6561.2.a.c.1.49		72	81.59	odd	54
6561.2.a.d.1.24		72	81.22	even	27

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)

\(f(q)\)	\(=\)	\(q+(0.0484354 + 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(1.17364 + 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(0.478230 + 2.71217i) q^{8} +O(q^{10})\)	\(q+(0.0484354 + 0.831603i) q^{2} +(1.29726 - 0.151628i) q^{4} +(1.17364 + 0.278158i) q^{5} +(-0.785201 + 1.05471i) q^{7} +(0.478230 + 2.71217i) q^{8} +(-0.174471 + 0.989477i) q^{10} +(1.49146 + 1.58086i) q^{11} +(4.07045 - 2.04426i) q^{13} +(-0.915130 - 0.601890i) q^{14} +(0.309479 - 0.0733479i) q^{16} +(-3.54217 + 1.28924i) q^{17} +(-2.50517 - 0.911807i) q^{19} +(1.56469 + 0.182886i) q^{20} +(-1.24241 + 1.31687i) q^{22} +(3.60284 + 4.83945i) q^{23} +(-3.16810 - 1.59108i) q^{25} +(1.89717 + 3.28599i) q^{26} +(-0.858686 + 1.48729i) q^{28} +(-3.47381 + 2.28476i) q^{29} +(2.95363 - 6.84728i) q^{31} +(1.65571 + 5.53044i) q^{32} +(-1.24371 - 2.88323i) q^{34} +(-1.21492 + 1.01944i) q^{35} +(7.47819 + 6.27494i) q^{37} +(0.636923 - 2.12747i) q^{38} +(-0.193143 + 3.31614i) q^{40} +(0.336547 - 5.77829i) q^{41} +(1.44983 - 4.84276i) q^{43} +(2.17451 + 1.82463i) q^{44} +(-3.85000 + 3.23053i) q^{46} +(1.18743 + 2.75276i) q^{47} +(1.51175 + 5.04961i) q^{49} +(1.16970 - 2.71167i) q^{50} +(4.97047 - 3.26913i) q^{52} +(6.22987 - 10.7905i) q^{53} +(1.31071 + 2.27022i) q^{55} +(-3.23606 - 1.62521i) q^{56} +(-2.06827 - 2.77817i) q^{58} +(-7.48542 + 7.93408i) q^{59} +(-11.7134 - 1.36910i) q^{61} +(5.83728 + 2.12460i) q^{62} +(-3.92120 + 1.42720i) q^{64} +(5.34588 - 1.26700i) q^{65} +(0.693545 + 0.456152i) q^{67} +(-4.39962 + 2.20957i) q^{68} +(-0.906613 - 0.960954i) q^{70} +(-1.25916 + 7.14107i) q^{71} +(-1.41006 - 7.99685i) q^{73} +(-4.85605 + 6.52281i) q^{74} +(-3.38811 - 0.802996i) q^{76} +(-2.83844 + 0.331766i) q^{77} +(0.668640 + 11.4801i) q^{79} +0.383620 q^{80} +4.82155 q^{82} +(-0.277632 - 4.76675i) q^{83} +(-4.51585 + 0.527827i) q^{85} +(4.09748 + 0.971120i) q^{86} +(-3.57430 + 4.80112i) q^{88} +(-0.578632 - 3.28158i) q^{89} +(-1.04003 + 5.89829i) q^{91} +(5.40761 + 5.73174i) q^{92} +(-2.23169 + 1.12080i) q^{94} +(-2.68654 - 1.76697i) q^{95} +(1.32651 - 0.314388i) q^{97} +(-4.12605 + 1.50176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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