LMFDB - Embedded newform 729.2.c.a.244.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.2
Root			$-1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.a.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06251 - 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(-1.03547 + 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} +1.09598 q^{8} +O(q^{10})$	\(q+(-1.06251 - 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(-1.03547 + 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} +1.09598 q^{8} +4.40081 q^{10} +(2.07474 + 3.59356i) q^{11} +(0.608008 - 1.05310i) q^{13} +(-5.15178 + 8.92315i) q^{14} +(1.35126 + 2.34044i) q^{16} -2.36364 q^{17} -1.83801 q^{19} +(-2.60498 - 4.51196i) q^{20} +(4.40889 - 7.63642i) q^{22} +(-2.15178 + 3.72700i) q^{23} +(0.355603 + 0.615922i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(1.49091 + 2.58233i) q^{29} +(-0.736793 + 1.27616i) q^{31} +(3.96743 - 6.87180i) q^{32} +(2.51140 + 4.34987i) q^{34} +10.0413 q^{35} +8.97108 q^{37} +(1.95291 + 3.38254i) q^{38} +(-1.13485 + 1.96562i) q^{40} +(1.13026 - 1.95767i) q^{41} +(2.74243 + 4.75003i) q^{43} -10.4391 q^{44} +9.14521 q^{46} +(3.59157 + 6.22077i) q^{47} +(-8.25481 + 14.2978i) q^{49} +(0.755667 - 1.30885i) q^{50} +(1.52959 + 2.64933i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(-2.65702 - 4.60209i) q^{56} +(3.16823 - 5.48753i) q^{58} +(0.131128 - 0.227121i) q^{59} +(2.22780 + 3.85867i) q^{61} +3.13141 q^{62} -11.4568 q^{64} +(1.25915 + 2.18091i) q^{65} +(-2.06555 + 3.57764i) q^{67} +(2.97316 - 5.14966i) q^{68} +(-10.6690 - 18.4793i) q^{70} -3.08551 q^{71} +12.7601 q^{73} +(-9.53190 - 16.5097i) q^{74} +(2.31198 - 4.00447i) q^{76} +(10.0598 - 17.4240i) q^{77} +(-2.27620 - 3.94250i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(-4.22653 - 7.32056i) q^{83} +(2.44748 - 4.23915i) q^{85} +(5.82774 - 10.0939i) q^{86} +(2.27387 + 3.93846i) q^{88} -16.9632 q^{89} -5.89606 q^{91} +(-5.41335 - 9.37619i) q^{92} +(7.63218 - 13.2193i) q^{94} +(1.90320 - 3.29644i) q^{95} +(2.55489 + 4.42519i) q^{97} +35.0834 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.06251	−	1.84033i	−0.751311	−	1.30131i	−0.947187	−	0.320680i	$-0.896088\pi$
$2$	−1.06251	−	1.84033i	−0.751311	−	1.30131i	0.195876	−	0.980629i	$-0.437245\pi$
$3$		0			0
$3$		0			0
$4$	−1.25787	+	2.17870i	−0.628937	+	1.08935i
$5$	−1.03547	+	1.79349i	−0.463076	+	0.802072i	−0.999112	−	0.0421233i	$-0.986588\pi$
$5$	−1.03547	+	1.79349i	−0.463076	+	0.802072i	0.536036	+	0.844195i	$0.319921\pi$
$6$		0			0
$7$	−2.42434	−	4.19907i	−0.916313	−	1.58710i	−0.804967	−	0.593319i	$-0.797817\pi$
$7$	−2.42434	−	4.19907i	−0.916313	−	1.58710i	−0.111346	−	0.993782i	$-0.535516\pi$
$8$	1.09598			0.387487
$9$		0			0
$10$	4.40081			1.39166
$11$	2.07474	+	3.59356i	0.625559	+	1.08350i	0.988432	+	0.151662i	$0.0484624\pi$
$11$	2.07474	+	3.59356i	0.625559	+	1.08350i	−0.362874	+	0.931838i	$0.618204\pi$
$12$		0			0
$13$	0.608008	−	1.05310i	0.168631	−	0.292077i	−0.769308	−	0.638878i	$-0.779399\pi$
$13$	0.608008	−	1.05310i	0.168631	−	0.292077i	0.937939	+	0.346801i	$0.112732\pi$
$14$	−5.15178	+	8.92315i	−1.37687	+	2.38481i
$15$		0			0
$16$	1.35126	+	2.34044i	0.337814	+	0.585111i
$17$	−2.36364			−0.573266			−0.286633	−	0.958040i	$-0.592536\pi$
$17$	−2.36364			−0.573266			−0.286633	+	0.958040i	$0.592536\pi$
$18$		0			0
$19$	−1.83801			−0.421668			−0.210834	−	0.977522i	$-0.567618\pi$
$19$	−1.83801			−0.421668			−0.210834	+	0.977522i	$0.567618\pi$
$20$	−2.60498	−	4.51196i	−0.582491	−	1.00890i
$21$		0			0
$22$	4.40889	−	7.63642i	0.939979	−	1.62809i
$23$	−2.15178	+	3.72700i	−0.448678	+	0.777133i	−0.998300	−	0.0582801i	$-0.981438\pi$
$23$	−2.15178	+	3.72700i	−0.448678	+	0.777133i	0.549622	+	0.835413i	$0.314772\pi$
$24$		0			0
$25$	0.355603	+	0.615922i	0.0711206	+	0.123184i
$26$	−2.58407			−0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	1.49091	+	2.58233i	0.276855	+	0.479527i	0.970601	−	0.240692i	$-0.0773745\pi$
$29$	1.49091	+	2.58233i	0.276855	+	0.479527i	−0.693746	+	0.720219i	$0.744041\pi$
$30$		0			0
$31$	−0.736793	+	1.27616i	−0.132332	+	0.229206i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$	−0.736793	+	1.27616i	−0.132332	+	0.229206i	0.792243	+	0.610206i	$0.208913\pi$
$32$	3.96743	−	6.87180i	0.701350	−	1.21477i
$33$		0			0
$34$	2.51140	+	4.34987i	0.430701	+	0.745997i
$35$	10.0413			1.69729
$36$		0			0
$37$	8.97108			1.47484			0.737418	−	0.675436i	$-0.236045\pi$
$37$	8.97108			1.47484			0.737418	+	0.675436i	$0.236045\pi$
$38$	1.95291	+	3.38254i	0.316804	+	0.548720i
$39$		0			0
$40$	−1.13485	+	1.96562i	−0.179436	+	0.310792i
$41$	1.13026	−	1.95767i	0.176517	−	0.305737i	−0.764168	−	0.645017i	$-0.776850\pi$
$41$	1.13026	−	1.95767i	0.176517	−	0.305737i	0.940685	+	0.339280i	$0.110184\pi$
$42$		0			0
$43$	2.74243	+	4.75003i	0.418216	+	0.724372i	0.995760	−	0.0919876i	$-0.0293220\pi$
$43$	2.74243	+	4.75003i	0.418216	+	0.724372i	−0.577544	+	0.816360i	$0.695989\pi$
$44$	−10.4391			−1.57375
$45$		0			0
$46$	9.14521			1.34839
$47$	3.59157	+	6.22077i	0.523884	+	0.907393i	0.999613	+	0.0278017i	$0.00885069\pi$
$47$	3.59157	+	6.22077i	0.523884	+	0.907393i	−0.475730	+	0.879591i	$0.657816\pi$
$48$		0			0
$49$	−8.25481	+	14.2978i	−1.17926	+	2.04254i
$50$	0.755667	−	1.30885i	0.106867	−	0.185100i
$51$		0			0
$52$	1.52959	+	2.64933i	0.212116	+	0.367396i
$53$	6.32803			0.869222			0.434611	−	0.900618i	$-0.356886\pi$
$53$	6.32803			0.869222			0.434611	+	0.900618i	$0.356886\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	−2.65702	−	4.60209i	−0.355059	−	0.614980i
$57$		0			0
$58$	3.16823	−	5.48753i	0.416009	−	0.720548i
$59$	0.131128	−	0.227121i	0.0170715	−	0.0295686i	−0.857363	−	0.514711i	$-0.827899\pi$
$59$	0.131128	−	0.227121i	0.0170715	−	0.0295686i	0.874435	+	0.485143i	$0.161232\pi$
$60$		0			0
$61$	2.22780	+	3.85867i	0.285241	+	0.494052i	0.972668	−	0.232202i	$-0.0745931\pi$
$61$	2.22780	+	3.85867i	0.285241	+	0.494052i	−0.687427	+	0.726254i	$0.741260\pi$
$62$	3.13141			0.397690
$63$		0			0
$64$	−11.4568			−1.43210
$65$	1.25915	+	2.18091i	0.156178	+	0.270508i
$66$		0			0
$67$	−2.06555	+	3.57764i	−0.252347	+	0.437078i	−0.964172	−	0.265279i	$-0.914536\pi$
$67$	−2.06555	+	3.57764i	−0.252347	+	0.437078i	0.711824	+	0.702358i	$0.247869\pi$
$68$	2.97316	−	5.14966i	0.360548	−	0.624488i
$69$		0			0
$70$	−10.6690	−	18.4793i	−1.27519	−	2.20870i
$71$	−3.08551			−0.366183			−0.183091	−	0.983096i	$-0.558610\pi$
$71$	−3.08551			−0.366183			−0.183091	+	0.983096i	$0.558610\pi$
$72$		0			0
$73$	12.7601			1.49345			0.746726	−	0.665132i	$-0.231625\pi$
$73$	12.7601			1.49345			0.746726	+	0.665132i	$0.231625\pi$
$74$	−9.53190	−	16.5097i	−1.10806	−	1.91922i
$75$		0			0
$76$	2.31198	−	4.00447i	0.265202	−	0.459344i
$77$	10.0598	−	17.4240i	1.14642	−	1.98565i
$78$		0			0
$79$	−2.27620	−	3.94250i	−0.256093	−	0.443566i	0.709099	−	0.705109i	$-0.249102\pi$
$79$	−2.27620	−	3.94250i	−0.256093	−	0.443566i	−0.965192	+	0.261543i	$0.915769\pi$
$80$	−5.59674			−0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	−4.22653	−	7.32056i	−0.463922	−	0.803536i	0.535230	−	0.844706i	$-0.320225\pi$
$83$	−4.22653	−	7.32056i	−0.463922	−	0.803536i	−0.999152	+	0.0411700i	$0.986891\pi$
$84$		0			0
$85$	2.44748	−	4.23915i	0.265466	−	0.459801i
$86$	5.82774	−	10.0939i	0.628421	−	1.08846i
$87$		0			0
$88$	2.27387	+	3.93846i	0.242396	+	0.419842i
$89$	−16.9632			−1.79809			−0.899046	−	0.437854i	$-0.855739\pi$
$89$	−16.9632			−1.79809			−0.899046	+	0.437854i	$0.855739\pi$
$90$		0			0
$91$	−5.89606			−0.618075
$92$	−5.41335	−	9.37619i	−0.564380	−	0.977535i
$93$		0			0
$94$	7.63218	−	13.2193i	0.787199	−	1.36347i
$95$	1.90320	−	3.29644i	0.195264	−	0.338208i
$96$		0			0
$97$	2.55489	+	4.42519i	0.259409	+	0.449310i	0.966084	−	0.258229i	$-0.0831388\pi$
$97$	2.55489	+	4.42519i	0.259409	+	0.449310i	−0.706674	+	0.707539i	$0.749805\pi$
$98$	35.0834			3.54396
$99$		0			0
$100$	−1.78921			−0.178921
$101$	9.28994	+	16.0906i	0.924384	+	1.60108i	0.792550	+	0.609808i	$0.208753\pi$
$101$	9.28994	+	16.0906i	0.924384	+	1.60108i	0.131834	+	0.991272i	$0.457913\pi$
$102$		0			0
$103$	−4.50288	+	7.79923i	−0.443682	+	0.768481i	−0.997959	−	0.0638518i	$-0.979662\pi$
$103$	−4.50288	+	7.79923i	−0.443682	+	0.768481i	0.554277	+	0.832332i	$0.312995\pi$
$104$	0.666363	−	1.15417i	0.0653422	−	0.113176i
$105$		0			0
$106$	−6.72362	−	11.6457i	−0.653056	−	1.13113i
$107$	−7.42680			−0.717976			−0.358988	−	0.933342i	$-0.616878\pi$
$107$	−7.42680			−0.717976			−0.358988	+	0.933342i	$0.616878\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	9.13055	+	15.8146i	0.870564	+	1.50786i
$111$		0			0
$112$	6.55179	−	11.3480i	0.619086	−	1.07229i
$113$	−1.20133	+	2.08077i	−0.113012	+	0.195743i	−0.916983	−	0.398926i	$-0.869383\pi$
$113$	−1.20133	+	2.08077i	−0.113012	+	0.195743i	0.803971	+	0.594668i	$0.202717\pi$
$114$		0			0
$115$	−4.45622	−	7.71839i	−0.415544	−	0.719744i
$116$	−7.50150			−0.696497
$117$		0			0
$118$	−0.557303			−0.0513039
$119$	5.73025	+	9.92509i	0.525292	+	0.909832i
$120$		0			0
$121$	−3.10913	+	5.38517i	−0.282648	+	0.489561i
$122$	4.73415	−	8.19978i	0.428609	−	0.742373i
$123$		0			0
$124$	−1.85359	−	3.21050i	−0.166457	−	0.288312i
$125$	−11.8276			−1.05789
$126$		0			0
$127$	−9.23469			−0.819447			−0.409723	−	0.912210i	$-0.634375\pi$
$127$	−9.23469			−0.819447			−0.409723	+	0.912210i	$0.634375\pi$
$128$	4.23815	+	7.34069i	0.374603	+	0.648831i
$129$		0			0
$130$	2.67572	−	4.63449i	0.234677	−	0.406472i
$131$	−7.66950	+	13.2840i	−0.670088	+	1.16063i	0.307791	+	0.951454i	$0.400410\pi$
$131$	−7.66950	+	13.2840i	−0.670088	+	1.16063i	−0.977879	+	0.209172i	$0.932923\pi$
$132$		0			0
$133$	4.45595	+	7.71792i	0.386380	+	0.669229i
$134$	8.77871			0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	−1.82198	−	3.15577i	−0.155663	−	0.269616i	0.777637	−	0.628713i	$-0.216418\pi$
$137$	−1.82198	−	3.15577i	−0.155663	−	0.269616i	−0.933300	+	0.359097i	$0.883085\pi$
$138$		0			0
$139$	−6.63777	+	11.4970i	−0.563008	+	0.975159i	0.434224	+	0.900805i	$0.357023\pi$
$139$	−6.63777	+	11.4970i	−0.563008	+	0.975159i	−0.997232	+	0.0743538i	$0.976311\pi$
$140$	−12.6307	+	21.8770i	−1.06749	+	1.84895i
$141$		0			0
$142$	3.27840	+	5.67835i	0.275117	+	0.476517i
$143$	5.04584			0.421954
$144$		0			0
$145$	−6.17517			−0.512820
$146$	−13.5577	−	23.4827i	−1.12205	−	1.94344i
$147$		0			0
$148$	−11.2845	+	19.5453i	−0.927579	+	1.60661i
$149$	4.45549	−	7.71714i	0.365008	−	0.632213i	−0.623769	−	0.781608i	$-0.714400\pi$
$149$	4.45549	−	7.71714i	0.365008	−	0.632213i	0.988777	+	0.149396i	$0.0477329\pi$
$150$		0			0
$151$	0.356202	+	0.616960i	0.0289873	+	0.0502075i	0.880155	−	0.474686i	$-0.157438\pi$
$151$	0.356202	+	0.616960i	0.0289873	+	0.0502075i	−0.851168	+	0.524894i	$0.824105\pi$
$152$	−2.01441			−0.163391
$153$		0			0
$154$	−42.7545			−3.44526
$155$	−1.52585	−	2.64286i	−0.122560	−	0.212279i
$156$		0			0
$157$	6.90903	−	11.9668i	0.551400	−	0.955054i	−0.446773	−	0.894647i	$-0.647427\pi$
$157$	6.90903	−	11.9668i	0.551400	−	0.955054i	0.998174	−	0.0604064i	$-0.0192397\pi$
$158$	−4.83700	+	8.37793i	−0.384811	+	0.666512i
$159$		0			0
$160$	8.21632	+	14.2311i	0.649557	+	1.12507i
$161$	20.8666			1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	2.84345	+	4.92501i	0.222036	+	0.384578i
$165$		0			0
$166$	−8.98150	+	15.5564i	−0.697099	+	1.20741i
$167$	−11.9682	+	20.7295i	−0.926124	+	1.60409i	−0.136381	+	0.990657i	$0.543547\pi$
$167$	−11.9682	+	20.7295i	−0.926124	+	1.60409i	−0.789743	+	0.613437i	$0.789786\pi$
$168$		0			0
$169$	5.76065	+	9.97774i	0.443127	+	0.767519i
$170$	−10.4019			−0.797791
$171$		0			0
$172$	−13.7985			−1.05213
$173$	−4.57000	−	7.91547i	−0.347451	−	0.601802i	0.638345	−	0.769750i	$-0.279619\pi$
$173$	−4.57000	−	7.91547i	−0.347451	−	0.601802i	−0.985796	+	0.167948i	$0.946286\pi$
$174$		0			0
$175$	1.72420	−	2.98641i	0.130337	−	0.225751i
$176$	−5.60702	+	9.71164i	−0.422645	+	0.732043i
$177$		0			0
$178$	18.0236	+	31.2178i	1.35093	+	2.33987i
$179$	−10.6008			−0.792337			−0.396169	−	0.918178i	$-0.629660\pi$
$179$	−10.6008			−0.792337			−0.396169	+	0.918178i	$0.629660\pi$
$180$		0			0
$181$	−1.46292			−0.108738			−0.0543690	−	0.998521i	$-0.517315\pi$
$181$	−1.46292			−0.108738			−0.0543690	+	0.998521i	$0.517315\pi$
$182$	6.26465	+	10.8507i	0.464367	+	0.804307i
$183$		0			0
$184$	−2.35831	+	4.08471i	−0.173857	+	0.301129i
$185$	−9.28929	+	16.0895i	−0.682962	+	1.18292i
$186$		0			0
$187$	−4.90395	−	8.49388i	−0.358612	−	0.621134i
$188$	−18.0709			−1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	6.21114	+	10.7580i	0.449422	+	0.778422i	0.998348	−	0.0574488i	$-0.0182966\pi$
$191$	6.21114	+	10.7580i	0.449422	+	0.778422i	−0.548926	+	0.835871i	$0.684963\pi$
$192$		0			0
$193$	−10.3867	+	17.9902i	−0.747647	+	1.29496i	0.201300	+	0.979530i	$0.435483\pi$
$193$	−10.3867	+	17.9902i	−0.747647	+	1.29496i	−0.948948	+	0.315434i	$0.897850\pi$
$194$	5.42921	−	9.40366i	0.389794	−	0.675143i
$195$		0			0
$196$	−20.7670	−	35.9695i	−1.48336	−	2.56925i
$197$	14.1887			1.01090			0.505450	−	0.862856i	$-0.331326\pi$
$197$	14.1887			1.01090			0.505450	+	0.862856i	$0.331326\pi$
$198$		0			0
$199$	20.3286			1.44106			0.720529	−	0.693424i	$-0.243899\pi$
$199$	20.3286			1.44106			0.720529	+	0.693424i	$0.243899\pi$
$200$	0.389733	+	0.675037i	0.0275583	+	0.0477323i
$201$		0			0
$202$	19.7414	−	34.1931i	1.38900	−	2.40582i
$203$	7.22893	−	12.5209i	0.507372	−	0.878794i
$204$		0			0
$205$	2.34071	+	4.05422i	0.163482	+	0.283159i
$206$	19.1375			1.33337
$207$		0			0
$208$	3.28629			0.227864
$209$	−3.81339	−	6.60499i	−0.263778	−	0.456877i
$210$		0			0
$211$	4.93166	−	8.54189i	0.339509	−	0.588048i	−0.644831	−	0.764325i	$-0.723072\pi$
$211$	4.93166	−	8.54189i	0.339509	−	0.588048i	0.984341	+	0.176278i	$0.0564056\pi$
$212$	−7.95986	+	13.7869i	−0.546685	+	0.946887i
$213$		0			0
$214$	7.89109	+	13.6678i	0.539424	+	0.934309i
$215$	−11.3588			−0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	5.97554	+	10.3499i	0.404715	+	0.700986i
$219$		0			0
$220$	10.8093	−	18.7223i	0.728766	−	1.26226i
$221$	−1.43711	+	2.48915i	−0.0966705	+	0.167438i
$222$		0			0
$223$	−7.53569	−	13.0522i	−0.504627	−	0.874040i	−0.999986	−	0.00535136i	$-0.998297\pi$
$223$	−7.53569	−	13.0522i	−0.504627	−	0.874040i	0.495358	−	0.868689i	$-0.335037\pi$
$224$	−38.4736			−2.57062
$225$		0			0
$226$	5.10574			0.339629
$227$	−11.3463	−	19.6523i	−0.753079	−	1.30437i	−0.946324	−	0.323221i	$-0.895234\pi$
$227$	−11.3463	−	19.6523i	−0.753079	−	1.30437i	0.193245	−	0.981151i	$-0.438099\pi$
$228$		0			0
$229$	−4.35835	+	7.54888i	−0.288008	+	0.498844i	−0.973334	−	0.229392i	$-0.926326\pi$
$229$	−4.35835	+	7.54888i	−0.288008	+	0.498844i	0.685326	+	0.728236i	$0.259660\pi$
$230$	−9.46959	+	16.4018i	−0.624406	+	1.08150i
$231$		0			0
$232$	1.63400	+	2.83018i	0.107278	+	0.185810i
$233$	23.5890			1.54536			0.772682	−	0.634793i	$-0.218915\pi$
$233$	23.5890			1.54536			0.772682	+	0.634793i	$0.218915\pi$
$234$		0			0
$235$	−14.8758			−0.970393
$236$	0.329886	+	0.571379i	0.0214737	+	0.0371936i
$237$		0			0
$238$	12.1770	−	21.0911i	0.789315	−	1.36713i
$239$	4.97726	−	8.62086i	0.321952	−	0.557637i	−0.658939	−	0.752197i	$-0.728994\pi$
$239$	4.97726	−	8.62086i	0.321952	−	0.557637i	0.980891	+	0.194559i	$0.0623277\pi$
$240$		0			0
$241$	−2.85672	−	4.94799i	−0.184018	−	0.318728i	0.759227	−	0.650826i	$-0.225577\pi$
$241$	−2.85672	−	4.94799i	−0.184018	−	0.318728i	−0.943245	+	0.332097i	$0.892244\pi$
$242$	13.2140			0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	−17.0952	−	29.6098i	−1.09217	−	1.89170i
$246$		0			0
$247$	−1.11752	+	1.93560i	−0.0711062	+	0.123160i
$248$	−0.807509	+	1.39865i	−0.0512769	+	0.0888141i
$249$		0			0
$250$	12.5670	+	21.7666i	0.794804	+	1.37664i
$251$	7.28966			0.460120			0.230060	−	0.973176i	$-0.426108\pi$
$251$	7.28966			0.460120			0.230060	+	0.973176i	$0.426108\pi$
$252$		0			0
$253$	−17.8576			−1.12270
$254$	9.81199	+	16.9949i	0.615659	+	1.06635i
$255$		0			0
$256$	−2.45062	+	4.24459i	−0.153163	+	0.265287i
$257$	−11.6215	+	20.1291i	−0.724932	+	1.25562i	0.234071	+	0.972220i	$0.424795\pi$
$257$	−11.6215	+	20.1291i	−0.724932	+	1.25562i	−0.959002	+	0.283399i	$0.908538\pi$
$258$		0			0
$259$	−21.7489	−	37.6702i	−1.35141	−	2.34071i
$260$	−6.33539			−0.392904
$261$		0			0
$262$	32.5958			2.01378
$263$	−13.6998	−	23.7288i	−0.844766	−	1.46318i	−0.885824	−	0.464021i	$-0.846406\pi$
$263$	−13.6998	−	23.7288i	−0.844766	−	1.46318i	0.0410581	−	0.999157i	$-0.486927\pi$
$264$		0			0
$265$	−6.55249	+	11.3492i	−0.402516	+	0.697178i
$266$	9.46901	−	16.4008i	0.580582	−	1.00560i
$267$		0			0
$268$	−5.19641	−	9.00044i	−0.317421	−	0.549789i
$269$	−9.41973			−0.574331			−0.287166	−	0.957881i	$-0.592713\pi$
$269$	−9.41973			−0.574331			−0.287166	+	0.957881i	$0.592713\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	−3.19388	−	5.53196i	−0.193657	−	0.335424i
$273$		0			0
$274$	−3.87177	+	6.70610i	−0.233902	+	0.405131i
$275$	−1.47557	+	2.55576i	−0.0889803	+	0.154118i
$276$		0			0
$277$	−0.187406	−	0.324597i	−0.0112601	−	0.0195031i	0.860340	−	0.509720i	$-0.170251\pi$
$277$	−0.187406	−	0.324597i	−0.0112601	−	0.0195031i	−0.871601	+	0.490217i	$0.836918\pi$
$278$	28.2109			1.69198
$279$		0			0
$280$	11.0051			0.657678
$281$	6.99079	+	12.1084i	0.417036	+	0.722327i	0.995640	−	0.0932815i	$-0.0297357\pi$
$281$	6.99079	+	12.1084i	0.417036	+	0.722327i	−0.578604	+	0.815609i	$0.696402\pi$
$282$		0			0
$283$	−7.78094	+	13.4770i	−0.462529	+	0.801124i	−0.999086	−	0.0427401i	$-0.986391\pi$
$283$	−7.78094	+	13.4770i	−0.462529	+	0.801124i	0.536557	+	0.843864i	$0.319725\pi$
$284$	3.88118	−	6.72240i	0.230306	−	0.398901i
$285$		0			0
$286$	−5.36128	−	9.28601i	−0.317019	−	0.549093i
$287$	−10.9605			−0.646980
$288$		0			0
$289$	−11.4132			−0.671366
$290$	6.56121	+	11.3643i	0.385287	+	0.667337i
$291$		0			0
$292$	−16.0505	+	27.8004i	−0.939287	+	1.62689i
$293$	12.3121	−	21.3252i	0.719281	−	1.24583i	−0.242004	−	0.970275i	$-0.577805\pi$
$293$	12.3121	−	21.3252i	0.719281	−	1.24583i	0.961285	−	0.275556i	$-0.0888621\pi$
$294$		0			0
$295$	0.271559	+	0.470354i	0.0158108	+	0.0273851i
$296$	9.83210			0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	2.61660	+	4.53209i	0.151322	+	0.262097i
$300$		0			0
$301$	13.2971	−	23.0313i	0.766434	−	1.32750i
$302$	0.756939	−	1.31106i	0.0435570	−	0.0754429i
$303$		0			0
$304$	−2.48362	−	4.30175i	−0.142445	−	0.246722i
$305$	−9.22729			−0.528353
$306$		0			0
$307$	−20.3912			−1.16379			−0.581893	−	0.813265i	$-0.697688\pi$
$307$	−20.3912			−1.16379			−0.581893	+	0.813265i	$0.697688\pi$
$308$	25.3078	+	43.8344i	1.44205	+	2.49770i
$309$		0			0
$310$	−3.24249	+	5.61615i	−0.184161	+	0.318976i
$311$	11.0895	−	19.2076i	0.628828	−	1.08916i	−0.358959	−	0.933353i	$-0.616868\pi$
$311$	11.0895	−	19.2076i	0.628828	−	1.08916i	0.987787	−	0.155809i	$-0.0497986\pi$
$312$		0			0
$313$	5.58602	+	9.67527i	0.315740	+	0.546879i	0.979595	−	0.200984i	$-0.0644138\pi$
$313$	5.58602	+	9.67527i	0.315740	+	0.546879i	−0.663854	+	0.747862i	$0.731080\pi$
$314$	−29.3638			−1.65709
$315$		0			0
$316$	11.4527			0.644265
$317$	12.6083	+	21.8383i	0.708154	+	1.22656i	0.965541	+	0.260251i	$0.0838053\pi$
$317$	12.6083	+	21.8383i	0.708154	+	1.22656i	−0.257387	+	0.966309i	$0.582861\pi$
$318$		0			0
$319$	−6.18651	+	10.7154i	−0.346378	+	0.599945i
$320$	11.8632	−	20.5476i	0.663172	−	1.14865i
$321$		0			0
$322$	−22.1711	−	38.4014i	−1.23554	−	2.14003i
$323$	4.34438			0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	1.26781	+	2.19591i	0.0702173	+	0.121620i
$327$		0			0
$328$	1.23874	−	2.14556i	0.0683981	−	0.118469i
$329$	17.4143	−	30.1625i	0.960083	−	1.66291i
$330$		0			0
$331$	13.0828	+	22.6602i	0.719098	+	1.24551i	0.961357	+	0.275303i	$0.0887782\pi$
$331$	13.0828	+	22.6602i	0.719098	+	1.24551i	−0.242259	+	0.970212i	$0.577888\pi$
$332$	21.2658			1.16711
$333$		0			0
$334$	50.8654			2.78323
$335$	−4.27763	−	7.40908i	−0.233712	−	0.404801i
$336$		0			0
$337$	−5.47302	+	9.47956i	−0.298135	+	0.516384i	−0.975709	−	0.219070i	$-0.929698\pi$
$337$	−5.47302	+	9.47956i	−0.298135	+	0.516384i	0.677575	+	0.735454i	$0.263031\pi$
$338$	12.2416	−	21.2030i	0.665853	−	1.15329i
$339$		0			0
$340$	6.15723	+	10.6646i	0.333923	+	0.578371i
$341$	−6.11463			−0.331126
$342$		0			0
$343$	46.1091			2.48966
$344$	3.00564	+	5.20592i	0.162053	+	0.280684i
$345$		0			0
$346$	−9.71138	+	16.8206i	−0.522087	+	0.904282i
$347$	1.75669	−	3.04268i	0.0943040	−	0.163339i	−0.815014	−	0.579441i	$-0.803271\pi$
$347$	1.75669	−	3.04268i	0.0943040	−	0.163339i	0.909318	+	0.416102i	$0.136604\pi$
$348$		0			0
$349$	14.5984	+	25.2852i	0.781436	+	1.35349i	0.931105	+	0.364750i	$0.118846\pi$
$349$	14.5984	+	25.2852i	0.781436	+	1.35349i	−0.149670	+	0.988736i	$0.547821\pi$
$350$	−7.32796			−0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	−12.5384	−	21.7172i	−0.667352	−	1.15589i	−0.978642	−	0.205573i	$-0.934094\pi$
$353$	−12.5384	−	21.7172i	−0.667352	−	1.15589i	0.311290	−	0.950315i	$-0.399239\pi$
$354$		0			0
$355$	3.19495	−	5.53382i	0.169571	−	0.293705i
$356$	21.3375	−	36.9577i	1.13089	−	1.95875i
$357$		0			0
$358$	11.2635	+	19.5089i	0.595292	+	1.03108i
$359$	−4.20724			−0.222050			−0.111025	−	0.993818i	$-0.535413\pi$
$359$	−4.20724			−0.222050			−0.111025	+	0.993818i	$0.535413\pi$
$360$		0			0
$361$	−15.6217			−0.822196
$362$	1.55437	+	2.69225i	0.0816961	+	0.141502i
$363$		0			0
$364$	7.41650	−	12.8458i	0.388730	−	0.673300i
$365$	−13.2127	+	22.8850i	−0.691582	+	1.19786i
$366$		0			0
$367$	−8.74832	−	15.1525i	−0.456658	−	0.790956i	0.542123	−	0.840299i	$-0.317620\pi$
$367$	−8.74832	−	15.1525i	−0.456658	−	0.790956i	−0.998782	+	0.0493433i	$0.984287\pi$
$368$	−11.6304			−0.606279
$369$		0			0
$370$	39.4800			2.05247
$371$	−15.3413	−	26.5719i	−0.796479	−	1.37954i
$372$		0			0
$373$	14.8273	−	25.6816i	0.767728	−	1.32974i	−0.171065	−	0.985260i	$-0.554721\pi$
$373$	14.8273	−	25.6816i	0.767728	−	1.32974i	0.938792	−	0.344483i	$-0.111946\pi$
$374$	−10.4210	+	18.0497i	−0.538858	+	0.933330i
$375$		0			0
$376$	3.93627	+	6.81783i	0.202998	+	0.351603i
$377$	3.62594			0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	4.78797	+	8.29301i	0.245618	+	0.425422i
$381$		0			0
$382$	13.1988	−	22.8611i	0.675312	−	1.16967i
$383$	4.94839	−	8.57086i	0.252851	−	0.437950i	−0.711459	−	0.702728i	$-0.751965\pi$
$383$	4.94839	−	8.57086i	0.252851	−	0.437950i	0.964310	+	0.264777i	$0.0852985\pi$
$384$		0			0
$385$	20.8332	+	36.0841i	1.06176	+	1.83902i
$386$	44.1439			2.24686
$387$		0			0
$388$	−12.8549			−0.652608
$389$	−10.5574	−	18.2859i	−0.535281	−	0.927133i	−0.999150	−	0.0412294i	$-0.986873\pi$
$389$	−10.5574	−	18.2859i	−0.535281	−	0.927133i	0.463869	−	0.885904i	$-0.346461\pi$
$390$		0			0
$391$	5.08604	−	8.80928i	0.257212	−	0.445504i
$392$	−9.04709	+	15.6700i	−0.456947	+	0.791455i
$393$		0			0
$394$	−15.0757	−	26.1118i	−0.759501	−	1.31549i
$395$	9.42776			0.474362
$396$		0			0
$397$	−9.77909			−0.490799			−0.245399	−	0.969422i	$-0.578919\pi$
$397$	−9.77909			−0.490799			−0.245399	+	0.969422i	$0.578919\pi$
$398$	−21.5995	−	37.4114i	−1.08268	−	1.87526i
$399$		0			0
$400$	−0.961021	+	1.66454i	−0.0480510	+	0.0832268i
$401$	−9.56967	+	16.5752i	−0.477886	+	0.827724i	−0.999679	−	0.0253491i	$-0.991930\pi$
$401$	−9.56967	+	16.5752i	−0.477886	+	0.827724i	0.521792	+	0.853073i	$0.325264\pi$
$402$		0			0
$403$	0.895952	+	1.55183i	0.0446305	+	0.0773024i
$404$	−46.7423			−2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	18.6127	+	32.2381i	0.922597	+	1.59799i
$408$		0			0
$409$	−7.49778	+	12.9865i	−0.370741	+	0.642143i	−0.989680	−	0.143297i	$-0.954230\pi$
$409$	−7.49778	+	12.9865i	−0.370741	+	0.642143i	0.618938	+	0.785439i	$0.287563\pi$
$410$	4.97407	−	8.61534i	0.245652	−	0.425481i
$411$		0			0
$412$	−11.3281	−	19.6209i	−0.558096	−	0.966651i
$413$	−1.27160			−0.0625712
$414$		0			0
$415$	17.5058			0.859325
$416$	−4.82446	−	8.35621i	−0.236539	−	0.409697i
$417$		0			0
$418$	−8.10357	+	14.0358i	−0.396359	+	0.686513i
$419$	2.90590	−	5.03317i	0.141963	−	0.245886i	−0.786273	−	0.617879i	$-0.787992\pi$
$419$	2.90590	−	5.03317i	0.141963	−	0.245886i	0.928236	+	0.371993i	$0.121325\pi$
$420$		0			0
$421$	6.65676	+	11.5298i	0.324431	+	0.561930i	0.981397	−	0.191990i	$-0.0614940\pi$
$421$	6.65676	+	11.5298i	0.324431	+	0.561930i	−0.656966	+	0.753920i	$0.728161\pi$
$422$	−20.9598			−1.02031
$423$		0			0
$424$	6.93538			0.336812
$425$	−0.840517	−	1.45582i	−0.0407711	−	0.0706175i
$426$		0			0
$427$	10.8019	−	18.7094i	0.522740	−	0.905412i
$428$	9.34198	−	16.1808i	0.451562	−	0.782128i
$429$		0			0
$430$	12.0689	+	20.9040i	0.582014	+	1.00808i
$431$	36.4166			1.75413			0.877064	−	0.480374i	$-0.159499\pi$
$431$	36.4166			1.75413			0.877064	+	0.480374i	$0.159499\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	−7.59160	−	13.1490i	−0.364408	−	0.631174i
$435$		0			0
$436$	7.07423	−	12.2529i	0.338794	−	0.586809i
$437$	3.95499	−	6.85025i	0.189193	−	0.327692i
$438$		0			0
$439$	−4.72663	−	8.18677i	−0.225590	−	0.390733i	0.730906	−	0.682478i	$-0.239098\pi$
$439$	−4.72663	−	8.18677i	−0.225590	−	0.390733i	−0.956496	+	0.291745i	$0.905764\pi$
$440$	−9.41811			−0.448991
$441$		0			0
$442$	6.10780			0.290518
$443$	8.26196	+	14.3101i	0.392537	+	0.679895i	0.992783	−	0.119921i	$-0.0382640\pi$
$443$	8.26196	+	14.3101i	0.392537	+	0.679895i	−0.600246	+	0.799815i	$0.704931\pi$
$444$		0			0
$445$	17.5649	−	30.4232i	0.832654	−	1.44220i
$446$	−16.0136	+	27.7363i	−0.758264	+	1.31335i
$447$		0			0
$448$	27.7751	+	48.1080i	1.31225	+	2.27289i
$449$	4.74362			0.223865			0.111933	−	0.993716i	$-0.464296\pi$
$449$	4.74362			0.223865			0.111933	+	0.993716i	$0.464296\pi$
$450$		0			0
$451$	9.38002			0.441688
$452$	−3.02225	−	5.23470i	−0.142155	−	0.246219i
$453$		0			0
$454$	−24.1112	+	41.7618i	−1.13159	+	1.95998i
$455$	6.10519	−	10.5745i	0.286216	−	0.495741i
$456$		0			0
$457$	11.2043	+	19.4064i	0.524114	+	0.907792i	0.999606	+	0.0280718i	$0.00893670\pi$
$457$	11.2043	+	19.4064i	0.524114	+	0.907792i	−0.475492	+	0.879720i	$0.657730\pi$
$458$	18.5232			0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	−7.46113	−	12.9231i	−0.347499	−	0.601887i	0.638305	−	0.769783i	$-0.279636\pi$
$461$	−7.46113	−	12.9231i	−0.347499	−	0.601887i	−0.985805	+	0.167897i	$0.946302\pi$
$462$		0			0
$463$	7.42359	−	12.8580i	0.345003	−	0.597563i	−0.640351	−	0.768082i	$-0.721211\pi$
$463$	7.42359	−	12.8580i	0.345003	−	0.597563i	0.985354	+	0.170519i	$0.0545444\pi$
$464$	−4.02920	+	6.97878i	−0.187051	+	0.323982i
$465$		0			0
$466$	−25.0636	−	43.4114i	−1.16105	−	2.01100i
$467$	15.3514			0.710379			0.355190	−	0.934794i	$-0.384416\pi$
$467$	15.3514			0.710379			0.355190	+	0.934794i	$0.384416\pi$
$468$		0			0
$469$	20.0304			0.924917
$470$	15.8058	+	27.3764i	0.729067	+	1.26278i
$471$		0			0
$472$	0.143714	−	0.248920i	0.00661496	−	0.0114574i
$473$	−11.3797	+	19.7102i	−0.523238	+	0.906275i
$474$		0			0
$475$	−0.653601	−	1.13207i	−0.0299893	−	0.0519429i
$476$	−28.8317			−1.32150
$477$		0			0
$478$	−21.1536			−0.967545
$479$	5.22430	+	9.04876i	0.238705	+	0.413448i	0.960343	−	0.278822i	$-0.0899439\pi$
$479$	5.22430	+	9.04876i	0.238705	+	0.413448i	−0.721638	+	0.692270i	$0.756611\pi$
$480$		0			0
$481$	5.45449	−	9.44745i	0.248703	−	0.430766i
$482$	−6.07062	+	10.5146i	−0.276509	+	0.478928i
$483$		0			0
$484$	−7.82178	−	13.5477i	−0.355536	−	0.615806i
$485$	−10.5820			−0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	2.44162	+	4.22901i	0.110527	+	0.191438i
$489$		0			0
$490$	−36.3278	+	62.9217i	−1.64112	+	2.84251i
$491$	−5.38867	+	9.33345i	−0.243187	+	0.421213i	−0.961620	−	0.274383i	$-0.911526\pi$
$491$	−5.38867	+	9.33345i	−0.243187	+	0.421213i	0.718433	+	0.695596i	$0.244860\pi$
$492$		0			0
$493$	−3.52397	−	6.10370i	−0.158712	−	0.274897i
$494$	4.74953			0.213692
$495$		0			0
$496$	−3.98238			−0.178814
$497$	7.48032	+	12.9563i	0.335538	+	0.581169i
$498$		0			0
$499$	9.59359	−	16.6166i	0.429468	−	0.743861i	−0.567358	−	0.823471i	$-0.692034\pi$
$499$	9.59359	−	16.6166i	0.429468	−	0.743861i	0.996826	+	0.0796106i	$0.0253677\pi$
$500$	14.8776	−	25.7687i	0.665346	−	1.15241i
$501$		0			0
$502$	−7.74537	−	13.4154i	−0.345693	−	0.598758i
$503$	12.0251			0.536171			0.268086	−	0.963395i	$-0.413609\pi$
$503$	12.0251			0.536171			0.268086	+	0.963395i	$0.413609\pi$
$504$		0			0
$505$	−38.4778			−1.71224
$506$	18.9740	+	32.8639i	0.843496	+	1.46098i
$507$		0			0
$508$	11.6161	−	20.1196i	0.515380	−	0.892664i
$509$	−7.47651	+	12.9497i	−0.331391	+	0.573985i	−0.982785	−	0.184754i	$-0.940851\pi$
$509$	−7.47651	+	12.9497i	−0.331391	+	0.573985i	0.651394	+	0.758739i	$0.274184\pi$
$510$		0			0
$511$	−30.9347	−	53.5804i	−1.36847	−	2.37026i
$512$	27.3678			1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	−9.32521	−	16.1517i	−0.410918	−	0.711730i
$516$		0			0
$517$	−14.9032	+	25.8130i	−0.655440	+	1.13526i
$518$	−46.2171	+	80.0503i	−2.03066	+	3.51721i
$519$		0			0
$520$	1.38000	+	2.39023i	0.0605169	+	0.104818i
$521$	−37.4188			−1.63935			−0.819673	−	0.572832i	$-0.805845\pi$
$521$	−37.4188			−1.63935			−0.819673	+	0.572832i	$0.805845\pi$
$522$		0			0
$523$	−8.44979			−0.369483			−0.184742	−	0.982787i	$-0.559145\pi$
$523$	−8.44979			−0.369483			−0.184742	+	0.982787i	$0.559145\pi$
$524$	−19.2945	−	33.4191i	−0.842885	−	1.45992i
$525$		0			0
$526$	−29.1125	+	50.4243i	−1.26936	+	2.19860i
$527$	1.74151	−	3.01639i	0.0758615	−	0.131396i
$528$		0			0
$529$	2.23965	+	3.87918i	0.0973760	+	0.168660i
$530$	27.8484			1.20966
$531$		0			0
$532$	−22.4201			−0.972033
$533$	−1.37442	−	2.38056i	−0.0595326	−	0.103113i
$534$		0			0
$535$	7.69023	−	13.3199i	0.332478	−	0.575868i
$536$	−2.26380	+	3.92101i	−0.0977812	+	0.169362i
$537$		0			0
$538$	10.0086	+	17.3354i	0.431501	+	0.747382i
$539$	−68.5065			−2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	−27.9225	−	48.3633i	−1.19938	−	2.07738i
$543$		0			0
$544$	−9.37758	+	16.2424i	−0.402060	+	0.696389i
$545$	5.82345	−	10.0865i	0.249449	−	0.432058i
$546$		0			0
$547$	−15.6975	−	27.1889i	−0.671178	−	1.16251i	−0.977570	−	0.210609i	$-0.932455\pi$
$547$	−15.6975	−	27.1889i	−0.671178	−	1.16251i	0.306393	−	0.951905i	$-0.400878\pi$
$548$	9.16731			0.391608
$549$		0			0
$550$	6.27126			0.267407
$551$	−2.74030	−	4.74634i	−0.116741	−	0.202201i
$552$		0			0
$553$	−11.0366	+	19.1159i	−0.469322	+	0.812890i
$554$	−0.398243	+	0.689777i	−0.0169197	+	0.0293058i
$555$		0			0
$556$	−16.6989	−	28.9234i	−0.708193	−	1.22663i
$557$	15.9303			0.674988			0.337494	−	0.941328i	$-0.390421\pi$
$557$	15.9303			0.674988			0.337494	+	0.941328i	$0.390421\pi$
$558$		0			0
$559$	6.66967			0.282097
$560$	13.5684	+	23.5011i	0.573369	+	0.993103i
$561$		0			0
$562$	14.8556	−	25.7307i	0.626647	−	1.08538i
$563$	−12.4304	+	21.5301i	−0.523880	+	0.907387i	0.475734	+	0.879589i	$0.342183\pi$
$563$	−12.4304	+	21.5301i	−0.523880	+	0.907387i	−0.999614	+	0.0277973i	$0.991151\pi$
$564$		0			0
$565$	−2.48789	−	4.30915i	−0.104666	−	0.181287i
$566$	33.0695			1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	9.59500	+	16.6190i	0.402243	+	0.696706i	0.993996	−	0.109413i	$-0.0348972\pi$
$569$	9.59500	+	16.6190i	0.402243	+	0.696706i	−0.591753	+	0.806119i	$0.701564\pi$
$570$		0			0
$571$	10.1896	−	17.6489i	0.426422	−	0.738585i	−0.570130	−	0.821555i	$-0.693107\pi$
$571$	10.1896	−	17.6489i	0.426422	−	0.738585i	0.996552	+	0.0829696i	$0.0264404\pi$
$572$	−6.34703	+	10.9934i	−0.265383	+	0.459656i
$573$		0			0
$574$	11.6457	+	20.1710i	0.486084	+	0.841921i
$575$	−3.06072			−0.127641
$576$		0			0
$577$	23.2991			0.969953			0.484976	−	0.874527i	$-0.338828\pi$
$577$	23.2991			0.969953			0.484976	+	0.874527i	$0.338828\pi$
$578$	12.1267	+	21.0041i	0.504404	+	0.873654i
$579$		0			0
$580$	7.76758	−	13.4539i	0.322531	−	0.558641i
$581$	−20.4931	+	35.4950i	−0.850195	+	1.47258i
$582$		0			0
$583$	13.1290	+	22.7402i	0.543749	+	0.941802i
$584$	13.9847			0.578693
$585$		0			0
$586$	−52.3272			−2.16162
$587$	−18.4546	−	31.9644i	−0.761704	−	1.31931i	−0.941971	−	0.335693i	$-0.891030\pi$
$587$	−18.4546	−	31.9644i	−0.761704	−	1.31931i	0.180267	−	0.983618i	$-0.442304\pi$
$588$		0			0
$589$	1.35423	−	2.34560i	0.0558001	−	0.0966486i
$590$	0.577071	−	0.999516i	0.0237576	−	0.0411494i
$591$		0			0
$592$	12.1222	+	20.9963i	0.498220	+	0.862943i
$593$	−4.36830			−0.179385			−0.0896923	−	0.995970i	$-0.528588\pi$
$593$	−4.36830			−0.179385			−0.0896923	+	0.995970i	$0.528588\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	11.2089	+	19.4144i	0.459134	+	0.795244i
$597$		0			0
$598$	5.56036	−	9.63082i	0.227380	−	0.393833i
$599$	−15.6028	+	27.0249i	−0.637513	+	1.10421i	0.348463	+	0.937322i	$0.386704\pi$
$599$	−15.6028	+	27.0249i	−0.637513	+	1.10421i	−0.985977	+	0.166883i	$0.946630\pi$
$600$		0			0
$601$	−21.9686	−	38.0507i	−0.896116	−	1.55212i	−0.832417	−	0.554149i	$-0.813044\pi$
$601$	−21.9686	−	38.0507i	−0.896116	−	1.55212i	−0.0636987	−	0.997969i	$-0.520290\pi$
$602$	−56.5136			−2.30332
$603$		0			0
$604$	−1.79223			−0.0729247
$605$	−6.43882	−	11.1524i	−0.261775	−	0.453408i
$606$		0			0
$607$	−8.67933	+	15.0330i	−0.352283	+	0.610172i	−0.986649	−	0.162861i	$-0.947928\pi$
$607$	−8.67933	+	15.0330i	−0.352283	+	0.610172i	0.634366	+	0.773033i	$0.281261\pi$
$608$	−7.29217	+	12.6304i	−0.295736	+	0.512231i
$609$		0			0
$610$	9.80413	+	16.9813i	0.396958	+	0.687551i
$611$	8.73480			0.353372
$612$		0			0
$613$	−1.19805			−0.0483887			−0.0241944	−	0.999707i	$-0.507702\pi$
$613$	−1.19805			−0.0483887			−0.0241944	+	0.999707i	$0.507702\pi$
$614$	21.6659	+	37.5265i	0.874365	+	1.51444i
$615$		0			0
$616$	11.0253	−	19.0963i	0.444221	−	0.769413i
$617$	13.0069	−	22.5285i	0.523636	−	0.906965i	−0.475985	−	0.879453i	$-0.657908\pi$
$617$	13.0069	−	22.5285i	0.523636	−	0.906965i	0.999621	−	0.0275115i	$-0.00875828\pi$
$618$		0			0
$619$	−4.81567	−	8.34099i	−0.193558	−	0.335253i	0.752869	−	0.658171i	$-0.228670\pi$
$619$	−4.81567	−	8.34099i	−0.193558	−	0.335253i	−0.946427	+	0.322918i	$0.895336\pi$
$620$	7.67733			0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	41.1244	+	71.2296i	1.64762	+	2.85375i
$624$		0			0
$625$	10.4691	−	18.1330i	0.418763	−	0.725319i
$626$	11.8705	−	20.5602i	0.474439	−	0.821752i
$627$		0			0
$628$	17.3814	+	30.1054i	0.693592	+	1.20134i
$629$	−21.2044			−0.845474
$630$		0			0
$631$	−14.1673			−0.563992			−0.281996	−	0.959416i	$-0.590997\pi$
$631$	−14.1673			−0.563992			−0.281996	+	0.959416i	$0.590997\pi$
$632$	−2.49467	−	4.32089i	−0.0992325	−	0.171876i
$633$		0			0
$634$	26.7931	−	46.4069i	1.06409	−	1.84306i
$635$	9.56225	−	16.5623i	0.379466	−	0.657255i
$636$		0			0
$637$	10.0380	+	17.3863i	0.397719	+	0.688870i
$638$	26.2930			1.04095
$639$		0			0
$640$	−17.5539			−0.693879
$641$	11.1005	+	19.2266i	0.438442	+	0.759403i	0.997570	−	0.0696782i	$-0.0221973\pi$
$641$	11.1005	+	19.2266i	0.438442	+	0.759403i	−0.559128	+	0.829081i	$0.688864\pi$
$642$		0			0
$643$	−10.7684	+	18.6514i	−0.424664	+	0.735540i	−0.996389	−	0.0849056i	$-0.972941\pi$
$643$	−10.7684	+	18.6514i	−0.424664	+	0.735540i	0.571725	+	0.820445i	$0.306274\pi$
$644$	−26.2475	+	45.4621i	−1.03430	+	1.79146i
$645$		0			0
$646$	−4.61597	−	7.99509i	−0.181613	−	0.314563i
$647$	−13.4037			−0.526952			−0.263476	−	0.964666i	$-0.584869\pi$
$647$	−13.4037			−0.526952			−0.263476	+	0.964666i	$0.584869\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	−0.918902	−	1.59159i	−0.0360423	−	0.0624271i
$651$		0			0
$652$	1.50091	−	2.59966i	0.0587802	−	0.101810i
$653$	−9.45543	+	16.3773i	−0.370020	+	0.640893i	−0.989568	−	0.144066i	$-0.953982\pi$
$653$	−9.45543	+	16.3773i	−0.370020	+	0.640893i	0.619548	+	0.784958i	$0.287316\pi$
$654$		0			0
$655$	−15.8831	−	27.5103i	−0.620603	−	1.07492i
$656$	6.10909			0.238520
$657$		0			0
$658$	−74.0119			−2.88528
$659$	−0.0140907	−	0.0244058i	−0.000548897	−	0.000950717i	0.865751	−	0.500475i	$-0.166841\pi$
$659$	−0.0140907	−	0.0244058i	−0.000548897	−	0.000950717i	−0.866300	+	0.499525i	$0.833508\pi$
$660$		0			0
$661$	22.5209	−	39.0073i	0.875960	−	1.51721i	0.0202238	−	0.999795i	$-0.493562\pi$
$661$	22.5209	−	39.0073i	0.875960	−	1.51721i	0.855736	−	0.517412i	$-0.173105\pi$
$662$	27.8014	−	48.1535i	1.08053	−	1.87154i
$663$		0			0
$664$	−4.63218	−	8.02317i	−0.179763	−	0.311359i
$665$	−18.4560			−0.715693
$666$		0			0
$667$	−12.8325			−0.496875
$668$	−30.1089	−	52.1501i	−1.16495	−	2.01775i
$669$		0			0
$670$	−9.09010	+	15.7445i	−0.351181	+	0.608263i
$671$	−9.24424	+	16.0115i	−0.356870	+	0.618117i
$672$		0			0
$673$	4.87984	+	8.45214i	0.188104	+	0.325806i	0.944618	−	0.328172i	$-0.106432\pi$
$673$	4.87984	+	8.45214i	0.188104	+	0.325806i	−0.756514	+	0.653978i	$0.773099\pi$
$674$	23.2607			0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	20.4404	+	35.4038i	0.785588	+	1.36068i	0.928647	+	0.370964i	$0.120973\pi$
$677$	20.4404	+	35.4038i	0.785588	+	1.36068i	−0.143060	+	0.989714i	$0.545694\pi$
$678$		0			0
$679$	12.3878	−	21.4563i	0.475400	−	0.823417i
$680$	2.68238	−	4.64602i	0.102865	−	0.178167i
$681$		0			0
$682$	6.49688	+	11.2529i	0.248779	+	0.430897i
$683$	44.0251			1.68457			0.842287	−	0.539029i	$-0.181209\pi$
$683$	44.0251			1.68457			0.842287	+	0.539029i	$0.181209\pi$
$684$		0			0
$685$	7.54644			0.288335
$686$	−48.9916	−	84.8559i	−1.87051	−	3.23981i
$687$		0			0
$688$	−7.41144	+	12.8370i	−0.282559	+	0.489406i
$689$	3.84749	−	6.66405i	0.146578	−	0.253880i
$690$		0			0
$691$	−10.7758	−	18.6642i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$691$	−10.7758	−	18.6642i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967781\pi$
$692$	22.9939			0.874098
$693$		0			0
$694$	−7.46603			−0.283407
$695$	−13.7464	−	23.8095i	−0.521432	−	0.903146i
$696$		0			0
$697$	−2.67153	+	4.62723i	−0.101191	+	0.175269i
$698$	31.0221	−	53.7318i	1.17420	−	2.03378i
$699$		0			0
$700$	4.33766	+	7.51304i	0.163948	+	0.283966i
$701$	12.8521			0.485419			0.242709	−	0.970099i	$-0.421964\pi$
$701$	12.8521			0.485419			0.242709	+	0.970099i	$0.421964\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	−23.7699	−	41.1707i	−0.895863	−	1.55168i
$705$		0			0
$706$	−26.6445	+	46.1496i	−1.00278	+	1.73686i
$707$	45.0439	−	78.0183i	1.69405	−	2.93418i
$708$		0			0
$709$	24.8559	+	43.0516i	0.933481	+	1.61684i	0.777320	+	0.629105i	$0.216578\pi$
$709$	24.8559	+	43.0516i	0.933481	+	1.61684i	0.156161	+	0.987732i	$0.450088\pi$
$710$	−13.5787			−0.509601
$711$		0			0
$712$	−18.5912			−0.696737
$713$	−3.17084	−	5.49206i	−0.118749	−	0.205679i
$714$		0			0
$715$	−5.22482	+	9.04965i	−0.195397	+	0.338438i
$716$	13.3344	−	23.0959i	0.498330	−	0.863133i
$717$		0			0
$718$	4.47026	+	7.74271i	0.166828	+	0.288955i
$719$	5.63745			0.210242			0.105121	−	0.994459i	$-0.466477\pi$
$719$	5.63745			0.210242			0.105121	+	0.994459i	$0.466477\pi$
$720$		0			0
$721$	43.6660			1.62621
$722$	16.5983	+	28.7491i	0.617725	+	1.06993i
$723$		0			0
$724$	1.84017	−	3.18727i	0.0683893	−	0.118454i
$725$	−1.06034	+	1.83657i	−0.0393802	+	0.0682085i
$726$		0			0
$727$	22.7071	+	39.3299i	0.842161	+	1.45867i	0.888064	+	0.459720i	$0.152050\pi$
$727$	22.7071	+	39.3299i	0.842161	+	1.45867i	−0.0459026	+	0.998946i	$0.514616\pi$
$728$	−6.46195			−0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	−6.48211	−	11.2273i	−0.239749	−	0.415258i
$732$		0			0
$733$	12.8334	−	22.2281i	0.474013	−	0.821015i	−0.525544	−	0.850766i	$-0.676138\pi$
$733$	12.8334	−	22.2281i	0.474013	−	0.821015i	0.999557	+	0.0297511i	$0.00947148\pi$
$734$	−18.5904	+	32.1996i	−0.686185	+	1.18851i
$735$		0			0
$736$	17.0741	+	29.5733i	0.629361	+	1.09008i
$737$	−17.1420			−0.631433
$738$		0			0
$739$	−14.4553			−0.531745			−0.265873	−	0.964008i	$-0.585660\pi$
$739$	−14.4553			−0.531745			−0.265873	+	0.964008i	$0.585660\pi$
$740$	−23.3695	−	40.4772i	−0.859080	−	1.48797i
$741$		0			0
$742$	−32.6006	+	56.4660i	−1.19681	+	2.07293i
$743$	17.3969	−	30.1323i	0.638229	−	1.10545i	−0.347592	−	0.937646i	$-0.613001\pi$
$743$	17.3969	−	30.1323i	0.638229	−	1.10545i	0.985821	−	0.167799i	$-0.0536661\pi$
$744$		0			0
$745$	9.22706	+	15.9817i	0.338053	+	0.585525i
$746$	−63.0168			−2.30721
$747$		0			0
$748$	24.6742			0.902177
$749$	18.0051	+	31.1857i	0.657891	+	1.13950i
$750$		0			0
$751$	−9.05922	+	15.6910i	−0.330576	+	0.572574i	−0.982625	−	0.185603i	$-0.940576\pi$
$751$	−9.05922	+	15.6910i	−0.330576	+	0.572574i	0.652049	+	0.758177i	$0.273910\pi$
$752$	−9.70624	+	16.8117i	−0.353950	+	0.613060i
$753$		0			0
$754$	−3.85261	−	6.67292i	−0.140304	−	0.243013i
$755$	−1.47535			−0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	−22.2621	−	38.5592i	−0.808598	−	1.40053i
$759$		0			0
$760$	2.08587	−	3.61282i	0.0756623	−	0.131051i
$761$	−6.22221	+	10.7772i	−0.225555	+	0.390673i	−0.956486	−	0.291779i	$-0.905753\pi$
$761$	−6.22221	+	10.7772i	−0.225555	+	0.390673i	0.730931	+	0.682452i	$0.239086\pi$
$762$		0			0
$763$	13.6344	+	23.6154i	0.493598	+	0.854936i
$764$	−31.2513			−1.13063
$765$		0			0
$766$	−21.0309			−0.759878
$767$	−0.159454	−	0.276183i	−0.00575755	−	0.00997238i
$768$		0			0
$769$	20.4428	−	35.4079i	0.737186	−	1.27684i	−0.216572	−	0.976267i	$-0.569488\pi$
$769$	20.4428	−	35.4079i	0.737186	−	1.27684i	0.953758	−	0.300576i	$-0.0971790\pi$
$770$	44.2711	−	76.6797i	1.59542	−	2.76335i
$771$		0			0
$772$	−26.1302	−	45.2588i	−0.940446	−	1.62890i
$773$	36.4162			1.30980			0.654900	−	0.755716i	$-0.272711\pi$
$773$	36.4162			1.30980			0.654900	+	0.755716i	$0.272711\pi$
$774$		0			0
$775$	−1.04802			−0.0376461
$776$	2.80010	+	4.84991i	0.100518	+	0.174102i
$777$		0			0
$778$	−22.4347	+	38.8581i	−0.804324	+	1.39313i
$779$	−2.07743	+	3.59821i	−0.0744316	+	0.128919i
$780$		0			0
$781$	−6.40165	−	11.0880i	−0.229069	−	0.396759i
$782$	−21.6160			−0.772985
$783$		0			0
$784$	−44.6174			−1.59348
$785$	14.3082	+	24.7825i	0.510681	+	0.884525i
$786$		0			0
$787$	−9.17358	+	15.8891i	−0.327003	+	0.566385i	−0.981916	−	0.189319i	$-0.939372\pi$
$787$	−9.17358	+	15.8891i	−0.327003	+	0.566385i	0.654913	+	0.755704i	$0.272705\pi$
$788$	−17.8475	+	30.9128i	−0.635792	+	1.10122i
$789$		0			0
$790$	−10.0171	−	17.3502i	−0.356394	−	0.617292i
$791$	11.6498			0.414218
$792$		0			0
$793$	5.41808			0.192402
$794$	10.3904	+	17.9967i	0.368742	+	0.638681i
$795$		0			0
$796$	−25.5709	+	44.2900i	−0.906335	+	1.56982i
$797$	1.73246	−	3.00071i	0.0613670	−	0.106291i	−0.833710	−	0.552203i	$-0.813787\pi$
$797$	1.73246	−	3.00071i	0.0613670	−	0.106291i	0.895077	+	0.445912i	$0.147121\pi$
$798$		0			0
$799$	−8.48916	−	14.7037i	−0.300325	−	0.520178i
$800$	5.64333			0.199522
$801$		0			0
$802$	40.6716			1.43617
$803$	26.4739	+	45.8541i	0.934243	+	1.61816i
$804$		0			0
$805$	−21.6067	+	37.4240i	−0.761537	+	1.31902i
$806$	1.90392	−	3.29769i	0.0670628	−	0.116156i
$807$		0			0
$808$	10.1816	+	17.6350i	0.358186	+	0.620397i
$809$	24.8406			0.873348			0.436674	−	0.899620i	$-0.356156\pi$
$809$	24.8406			0.873348			0.436674	+	0.899620i	$0.356156\pi$
$810$		0			0
$811$	−40.3286			−1.41613			−0.708063	−	0.706149i	$-0.750431\pi$
$811$	−40.3286			−1.41613			−0.708063	+	0.706149i	$0.750431\pi$
$812$	18.1862	+	31.4994i	0.638209	+	1.10541i
$813$		0			0
$814$	39.5525	−	68.5070i	1.38632	−	2.40117i
$815$	1.23554	−	2.14001i	0.0432790	−	0.0749614i
$816$		0			0
$817$	−5.04060	−	8.73058i	−0.176348	−	0.305444i
$818$	31.8660			1.11417
$819$		0			0
$820$	−11.7772			−0.411279
$821$	20.0908	+	34.7983i	0.701174	+	1.21447i	0.968055	+	0.250740i	$0.0806739\pi$
$821$	20.0908	+	34.7983i	0.701174	+	1.21447i	−0.266880	+	0.963730i	$0.585993\pi$
$822$		0			0
$823$	23.9777	−	41.5306i	0.835810	−	1.44766i	−0.0575599	−	0.998342i	$-0.518332\pi$
$823$	23.9777	−	41.5306i	0.835810	−	1.44766i	0.893370	−	0.449323i	$-0.148335\pi$
$824$	−4.93506	+	8.54777i	−0.171921	+	0.297776i
$825$		0			0
$826$	1.35109	+	2.34016i	0.0470104	+	0.0814245i
$827$	5.00048			0.173884			0.0869419	−	0.996213i	$-0.472291\pi$
$827$	5.00048			0.173884			0.0869419	+	0.996213i	$0.472291\pi$
$828$		0			0
$829$	29.7037			1.03165			0.515826	−	0.856693i	$-0.327485\pi$
$829$	29.7037			1.03165			0.515826	+	0.856693i	$0.327485\pi$
$830$	−18.6001	−	32.2164i	−0.645620	−	1.11825i
$831$		0			0
$832$	−6.96582	+	12.0652i	−0.241496	+	0.418284i
$833$	19.5114	−	33.7947i	0.676030	−	1.17092i
$834$		0			0
$835$	−24.7853	−	42.9295i	−0.857732	−	1.48564i
$836$	19.1871			0.663599
$837$		0			0
$838$	−12.3502			−0.426632
$839$	−12.9523	−	22.4340i	−0.447162	−	0.774507i	0.551038	−	0.834480i	$-0.314232\pi$
$839$	−12.9523	−	22.4340i	−0.447162	−	0.774507i	−0.998200	+	0.0599731i	$0.980898\pi$
$840$		0			0
$841$	10.0544	−	17.4147i	0.346703	−	0.600507i
$842$	14.1458	−	24.5012i	0.487497	−	0.844369i
$843$		0			0
$844$	12.4068	+	21.4892i	0.427060	+	0.739690i
$845$	−23.8599			−0.820807
$846$		0			0
$847$	30.1503			1.03598
$848$	8.55078	+	14.8104i	0.293635	+	0.508591i
$849$		0			0
$850$	−1.78612	+	3.09365i	−0.0612635	+	0.106111i
$851$	−19.3038	+	33.4352i	−0.661727	+	1.14614i
$852$		0			0
$853$	2.49583	+	4.32290i	0.0854556	+	0.148013i	0.905585	−	0.424164i	$-0.139432\pi$
$853$	2.49583	+	4.32290i	0.0854556	+	0.148013i	−0.820130	+	0.572178i	$0.806099\pi$
$854$	−45.9086			−1.57096
$855$		0			0
$856$	−8.13961			−0.278206
$857$	−7.34151	−	12.7159i	−0.250781	−	0.434366i	0.712960	−	0.701205i	$-0.247354\pi$
$857$	−7.34151	−	12.7159i	−0.250781	−	0.434366i	−0.963741	+	0.266839i	$0.914021\pi$
$858$		0			0
$859$	8.74243	−	15.1423i	0.298288	−	0.516650i	−0.677457	−	0.735563i	$-0.736918\pi$
$859$	8.74243	−	15.1423i	0.298288	−	0.516650i	0.975744	+	0.218913i	$0.0702511\pi$
$860$	14.2880	−	24.7475i	0.487215	−	0.843881i
$861$		0			0
$862$	−38.6932	−	67.0186i	−1.31790	−	2.28266i
$863$	−6.33263			−0.215565			−0.107783	−	0.994174i	$-0.534375\pi$
$863$	−6.33263			−0.215565			−0.107783	+	0.994174i	$0.534375\pi$
$864$		0			0
$865$	18.9284			0.643585
$866$	11.5560	+	20.0157i	0.392691	+	0.680160i
$867$		0			0
$868$	−8.98743	+	15.5667i	−0.305053	+	0.528368i
$869$	9.44508	−	16.3594i	0.320402	−	0.554953i
$870$		0			0
$871$	2.51174	+	4.35047i	0.0851072	+	0.147410i
$872$	−6.16374			−0.208730
$873$		0			0
$874$	−16.8090			−0.568571
$875$	28.6740	+	49.6648i	0.969358	+	1.67898i
$876$		0			0
$877$	−16.2655	+	28.1727i	−0.549247	+	0.951323i	0.449080	+	0.893492i	$0.351752\pi$
$877$	−16.2655	+	28.1727i	−0.549247	+	0.951323i	−0.998326	+	0.0578315i	$0.981581\pi$
$878$	−10.0442	+	17.3971i	−0.338976	+	0.587124i
$879$		0			0
$880$	−11.6118	−	20.1122i	−0.391434	−	0.677983i
$881$	33.3599			1.12393			0.561963	−	0.827163i	$-0.310046\pi$
$881$	33.3599			1.12393			0.561963	+	0.827163i	$0.310046\pi$
$882$		0			0
$883$	−54.8511			−1.84589			−0.922944	−	0.384934i	$-0.874224\pi$
$883$	−54.8511			−1.84589			−0.922944	+	0.384934i	$0.874224\pi$
$884$	−3.61541	−	6.26207i	−0.121599	−	0.210616i
$885$		0			0
$886$	17.5569	−	30.4094i	0.589835	−	1.02162i
$887$	10.5239	−	18.2279i	0.353357	−	0.612032i	−0.633478	−	0.773760i	$-0.718373\pi$
$887$	10.5239	−	18.2279i	0.353357	−	0.612032i	0.986835	+	0.161728i	$0.0517067\pi$
$888$		0			0
$889$	22.3880	+	38.7772i	0.750870	+	1.30054i
$890$	−74.6516			−2.50233
$891$		0			0
$892$	37.9158			1.26951
$893$	−6.60132	−	11.4338i	−0.220905	−	0.382618i
$894$		0			0
$895$	10.9768	−	19.0123i	0.366913	−	0.635512i
$896$	20.5494	−	35.5926i	0.686507	−	1.18906i
$897$		0			0
$898$	−5.04016	−	8.72982i	−0.168192	−	0.291318i
$899$	−4.39397			−0.146547
$900$		0			0
$901$	−14.9572			−0.498296
$902$	−9.96641	−	17.2623i	−0.331845	−	0.574772i
$903$		0			0
$904$	−1.31664	+	2.28048i	−0.0437906	+	0.0758476i
$905$	1.51481	−	2.62373i	0.0503540	−	0.0872157i
$906$		0			0
$907$	−7.41902	−	12.8501i	−0.246344	−	0.426681i	0.716164	−	0.697932i	$-0.245896\pi$
$907$	−7.41902	−	12.8501i	−0.246344	−	0.426681i	−0.962509	+	0.271251i	$0.912563\pi$
$908$	57.0887			1.89456
$909$		0			0
$910$	−25.9474			−0.860149
$911$	9.01477	+	15.6140i	0.298673	+	0.517316i	0.975833	−	0.218520i	$-0.0701228\pi$
$911$	9.01477	+	15.6140i	0.298673	+	0.517316i	−0.677160	+	0.735836i	$0.736789\pi$
$912$		0			0
$913$	17.5379	−	30.3766i	0.580421	−	1.00532i
$914$	23.8094	−	41.2391i	0.787545	−	1.36407i
$915$		0			0
$916$	−10.9645	−	18.9911i	−0.362278	−	0.627483i
$917$	74.3738			2.45604
$918$		0			0
$919$	13.4881			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$919$	13.4881			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$920$	−4.88391	−	8.45919i	−0.161018	−	0.278891i
$921$		0			0
$922$	−15.8551	+	27.4619i	−0.522160	+	0.904408i
$923$	−1.87601	+	3.24935i	−0.0617497	+	0.106954i
$924$		0			0
$925$	3.19014	+	5.52549i	0.104891	+	0.181677i
$926$	−31.5507			−1.03682
$927$		0			0
$928$	23.6603			0.776689
$929$	−18.8106	−	32.5809i	−0.617155	−	1.06894i	−0.990002	−	0.141051i	$-0.954952\pi$
$929$	−18.8106	−	32.5809i	−0.617155	−	1.06894i	0.372847	−	0.927893i	$-0.378381\pi$
$930$		0			0
$931$	15.1724	−	26.2794i	0.497255	−	0.861272i
$932$	−29.6719	+	51.3933i	−0.971936	+	1.68344i
$933$		0			0
$934$	−16.3111	−	28.2517i	−0.533716	−	0.924423i
$935$	20.3116			0.664259
$936$		0			0
$937$	4.14458			0.135398			0.0676988	−	0.997706i	$-0.478434\pi$
$937$	4.14458			0.135398			0.0676988	+	0.997706i	$0.478434\pi$
$938$	−21.2826	−	36.8625i	−0.694900	−	1.20360i
$939$		0			0
$940$	18.7119	−	32.4100i	0.610316	−	1.05710i
$941$	−1.76516	+	3.05735i	−0.0575427	+	0.0996668i	−0.893362	−	0.449338i	$-0.851660\pi$
$941$	−1.76516	+	3.05735i	−0.0575427	+	0.0996668i	0.835819	+	0.549005i	$0.184993\pi$
$942$		0			0
$943$	4.86416	+	8.42497i	0.158399	+	0.274355i
$944$	0.708752			0.0230679
$945$		0			0
$946$	48.3643			1.57246
$947$	−7.12754	−	12.3453i	−0.231614	−	0.401167i	0.726669	−	0.686987i	$-0.241067\pi$
$947$	−7.12754	−	12.3453i	−0.231614	−	0.401167i	−0.958283	+	0.285820i	$0.907734\pi$
$948$		0			0
$949$	7.75822	−	13.4376i	0.251842	−	0.436204i
$950$	−1.38892	+	2.40568i	−0.0450625	+	0.0780506i
$951$		0			0
$952$	6.28023	+	10.8777i	0.203543	+	0.352547i
$953$	−11.6426			−0.377141			−0.188570	−	0.982060i	$-0.560385\pi$
$953$	−11.6426			−0.377141			−0.188570	+	0.982060i	$0.560385\pi$
$954$		0			0
$955$	−25.7258			−0.832467
$956$	12.5215	+	21.6879i	0.404975	+	0.701437i
$957$		0			0
$958$	11.1018	−	19.2289i	0.358683	−	0.621257i
$959$	−8.83421	+	15.3013i	−0.285271	+	0.494105i
$960$		0			0
$961$	14.4143	+	24.9663i	0.464976	+	0.805363i
$962$	−23.1819			−0.747414
$963$		0			0
$964$	14.3736			0.462942
$965$	−21.5101	−	37.2566i	−0.692436	−	1.19933i
$966$		0			0
$967$	−14.5341	+	25.1737i	−0.467384	+	0.809533i	−0.999306	−	0.0372608i	$-0.988137\pi$
$967$	−14.5341	+	25.1737i	−0.467384	+	0.809533i	0.531922	+	0.846794i	$0.321470\pi$
$968$	−3.40754	+	5.90202i	−0.109522	+	0.189698i
$969$		0			0
$970$	11.2436	+	19.4744i	0.361009	+	0.625286i
$971$	−47.5792			−1.52689			−0.763444	−	0.645874i	$-0.776493\pi$
$971$	−47.5792			−1.52689			−0.763444	+	0.645874i	$0.776493\pi$
$972$		0			0
$973$	64.3687			2.06357
$974$	17.1754	+	29.7487i	0.550336	+	0.953209i
$975$		0			0
$976$	−6.02066	+	10.4281i	−0.192717	+	0.333795i
$977$	3.05815	−	5.29687i	0.0978389	−	0.169462i	−0.812951	−	0.582332i	$-0.802140\pi$
$977$	3.05815	−	5.29687i	0.0978389	−	0.169462i	0.910790	+	0.412870i	$0.135474\pi$
$978$		0			0
$979$	−35.1942	−	60.9582i	−1.12481	−	1.94823i
$980$	86.0145			2.74763
$981$		0			0
$982$	22.9022			0.730837
$983$	5.32591	+	9.22474i	0.169870	+	0.294224i	0.938374	−	0.345621i	$-0.112332\pi$
$983$	5.32591	+	9.22474i	0.169870	+	0.294224i	−0.768504	+	0.639845i	$0.778999\pi$
$984$		0			0
$985$	−14.6919	+	25.4472i	−0.468124	+	0.810814i
$986$	−7.48854	+	12.9705i	−0.238484	+	0.413066i
$987$		0			0
$988$	−2.81140	−	4.86949i	−0.0894426	−	0.154919i
$989$	−23.6045			−0.750578
$990$		0			0
$991$	23.9856			0.761928			0.380964	−	0.924590i	$-0.375592\pi$
$991$	23.9856			0.761928			0.380964	+	0.924590i	$0.375592\pi$
$992$	5.84636	+	10.1262i	0.185622	+	0.321507i
$993$		0			0
$994$	15.8959	−	27.5325i	0.504187	−	0.873277i
$995$	−21.0497	+	36.4591i	−0.667320	+	1.15583i
$996$		0			0
$997$	−2.15709	−	3.73619i	−0.0683157	−	0.118326i	0.829844	−	0.557995i	$-0.188429\pi$
$997$	−2.15709	−	3.73619i	−0.0683157	−	0.118326i	−0.898160	+	0.439669i	$0.855096\pi$
$998$	−40.7733			−1.29066
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.a.244.2		12
3.2	odd	2		729.2.c.d.244.5		12
9.2	odd	6		729.2.c.d.487.5		12
9.4	even	3		729.2.a.e.1.5	yes	6
9.5	odd	6		729.2.a.b.1.2	✓	6
9.7	even	3	inner	729.2.c.a.487.2		12
27.2	odd	18		729.2.e.j.82.1		12
27.4	even	9		729.2.e.u.649.2		12
27.5	odd	18		729.2.e.s.163.2		12
27.7	even	9		729.2.e.l.568.1		12
27.11	odd	18		729.2.e.t.325.1		12
27.13	even	9		729.2.e.k.406.2		12
27.14	odd	18		729.2.e.t.406.1		12
27.16	even	9		729.2.e.k.325.2		12
27.20	odd	18		729.2.e.s.568.2		12
27.22	even	9		729.2.e.l.163.1		12
27.23	odd	18		729.2.e.j.649.1		12
27.25	even	9		729.2.e.u.82.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.2	✓	6	9.5	odd	6
729.2.a.e.1.5	yes	6	9.4	even	3
729.2.c.a.244.2		12	1.1	even	1	trivial
729.2.c.a.487.2		12	9.7	even	3	inner
729.2.c.d.244.5		12	3.2	odd	2
729.2.c.d.487.5		12	9.2	odd	6
729.2.e.j.82.1		12	27.2	odd	18
729.2.e.j.649.1		12	27.23	odd	18
729.2.e.k.325.2		12	27.16	even	9
729.2.e.k.406.2		12	27.13	even	9
729.2.e.l.163.1		12	27.22	even	9
729.2.e.l.568.1		12	27.7	even	9
729.2.e.s.163.2		12	27.5	odd	18
729.2.e.s.568.2		12	27.20	odd	18
729.2.e.t.325.1		12	27.11	odd	18
729.2.e.t.406.1		12	27.14	odd	18
729.2.e.u.82.2		12	27.25	even	9
729.2.e.u.649.2		12	27.4	even	9

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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06251 - 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(-1.03547 + 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} +1.09598 q^{8} +O(q^{10})\)	\(q+(-1.06251 - 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(-1.03547 + 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} +1.09598 q^{8} +4.40081 q^{10} +(2.07474 + 3.59356i) q^{11} +(0.608008 - 1.05310i) q^{13} +(-5.15178 + 8.92315i) q^{14} +(1.35126 + 2.34044i) q^{16} -2.36364 q^{17} -1.83801 q^{19} +(-2.60498 - 4.51196i) q^{20} +(4.40889 - 7.63642i) q^{22} +(-2.15178 + 3.72700i) q^{23} +(0.355603 + 0.615922i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(1.49091 + 2.58233i) q^{29} +(-0.736793 + 1.27616i) q^{31} +(3.96743 - 6.87180i) q^{32} +(2.51140 + 4.34987i) q^{34} +10.0413 q^{35} +8.97108 q^{37} +(1.95291 + 3.38254i) q^{38} +(-1.13485 + 1.96562i) q^{40} +(1.13026 - 1.95767i) q^{41} +(2.74243 + 4.75003i) q^{43} -10.4391 q^{44} +9.14521 q^{46} +(3.59157 + 6.22077i) q^{47} +(-8.25481 + 14.2978i) q^{49} +(0.755667 - 1.30885i) q^{50} +(1.52959 + 2.64933i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(-2.65702 - 4.60209i) q^{56} +(3.16823 - 5.48753i) q^{58} +(0.131128 - 0.227121i) q^{59} +(2.22780 + 3.85867i) q^{61} +3.13141 q^{62} -11.4568 q^{64} +(1.25915 + 2.18091i) q^{65} +(-2.06555 + 3.57764i) q^{67} +(2.97316 - 5.14966i) q^{68} +(-10.6690 - 18.4793i) q^{70} -3.08551 q^{71} +12.7601 q^{73} +(-9.53190 - 16.5097i) q^{74} +(2.31198 - 4.00447i) q^{76} +(10.0598 - 17.4240i) q^{77} +(-2.27620 - 3.94250i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(-4.22653 - 7.32056i) q^{83} +(2.44748 - 4.23915i) q^{85} +(5.82774 - 10.0939i) q^{86} +(2.27387 + 3.93846i) q^{88} -16.9632 q^{89} -5.89606 q^{91} +(-5.41335 - 9.37619i) q^{92} +(7.63218 - 13.2193i) q^{94} +(1.90320 - 3.29644i) q^{95} +(2.55489 + 4.42519i) q^{97} +35.0834 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

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