LMFDB - Embedded newform 729.2.c.e.244.4

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:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.4
Root			$0.500000 - 1.27297i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.e.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.400763 + 0.694143i) q^{2} +(0.678777 - 1.17568i) q^{4} +(1.37492 - 2.38143i) q^{5} +(-1.18842 - 2.05840i) q^{7} +2.69117 q^{8} +O(q^{10})$	\(q+(0.400763 + 0.694143i) q^{2} +(0.678777 - 1.17568i) q^{4} +(1.37492 - 2.38143i) q^{5} +(-1.18842 - 2.05840i) q^{7} +2.69117 q^{8} +2.20407 q^{10} +(0.125079 + 0.216644i) q^{11} +(-1.30599 + 2.26204i) q^{13} +(0.952548 - 1.64986i) q^{14} +(-0.279032 - 0.483297i) q^{16} -0.293377 q^{17} -2.78475 q^{19} +(-1.86653 - 3.23292i) q^{20} +(-0.100255 + 0.173646i) q^{22} +(3.34492 - 5.79357i) q^{23} +(-1.28081 - 2.21843i) q^{25} -2.09357 q^{26} -3.22668 q^{28} +(0.177529 + 0.307488i) q^{29} +(-1.38273 + 2.39496i) q^{31} +(2.91482 - 5.04862i) q^{32} +(-0.117575 - 0.203645i) q^{34} -6.53592 q^{35} -6.99238 q^{37} +(-1.11602 - 1.93301i) q^{38} +(3.70015 - 6.40884i) q^{40} +(4.85880 - 8.41569i) q^{41} +(-0.130353 - 0.225778i) q^{43} +0.339604 q^{44} +5.36209 q^{46} +(5.71278 + 9.89482i) q^{47} +(0.675331 - 1.16971i) q^{49} +(1.02661 - 1.77813i) q^{50} +(1.77295 + 3.07085i) q^{52} +5.43137 q^{53} +0.687897 q^{55} +(-3.19823 - 5.53950i) q^{56} +(-0.142294 + 0.246460i) q^{58} +(-2.98846 + 5.17617i) q^{59} +(5.92338 + 10.2596i) q^{61} -2.21660 q^{62} +3.55649 q^{64} +(3.59127 + 6.22026i) q^{65} +(-0.905151 + 1.56777i) q^{67} +(-0.199138 + 0.344916i) q^{68} +(-2.61936 - 4.53686i) q^{70} -0.370510 q^{71} +5.02679 q^{73} +(-2.80229 - 4.85371i) q^{74} +(-1.89022 + 3.27396i) q^{76} +(0.297293 - 0.514927i) q^{77} +(-0.401411 - 0.695264i) q^{79} -1.53459 q^{80} +7.78892 q^{82} +(1.37783 + 2.38646i) q^{83} +(-0.403370 + 0.698657i) q^{85} +(0.104482 - 0.180967i) q^{86} +(0.336610 + 0.583026i) q^{88} +10.4507 q^{89} +6.20825 q^{91} +(-4.54091 - 7.86509i) q^{92} +(-4.57895 + 7.93097i) q^{94} +(-3.82880 + 6.63168i) q^{95} +(7.41730 + 12.8471i) q^{97} +1.08259 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * 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 $

$2$	0.400763	+	0.694143i	0.283383	+	0.490833i	0.972216	−	0.234087i	$-0.0752101\pi$
$2$	0.400763	+	0.694143i	0.283383	+	0.490833i	−0.688833	+	0.724920i	$0.741877\pi$
$3$		0			0
$3$		0			0
$4$	0.678777	−	1.17568i	0.339389	−	0.587838i
$5$	1.37492	−	2.38143i	0.614883	−	1.06501i	−0.375522	−	0.926814i	$-0.622536\pi$
$5$	1.37492	−	2.38143i	0.614883	−	1.06501i	0.990405	−	0.138195i	$-0.0441302\pi$
$6$		0			0
$7$	−1.18842	−	2.05840i	−0.449179	−	0.778001i	0.549153	−	0.835722i	$-0.314950\pi$
$7$	−1.18842	−	2.05840i	−0.449179	−	0.778001i	−0.998333	+	0.0577201i	$0.981617\pi$
$8$	2.69117			0.951472
$9$		0			0
$10$	2.20407			0.696989
$11$	0.125079	+	0.216644i	0.0377129	+	0.0653206i	0.884266	−	0.466984i	$-0.154659\pi$
$11$	0.125079	+	0.216644i	0.0377129	+	0.0653206i	−0.846553	+	0.532305i	$0.821326\pi$
$12$		0			0
$13$	−1.30599	+	2.26204i	−0.362217	+	0.627378i	−0.988325	−	0.152358i	$-0.951313\pi$
$13$	−1.30599	+	2.26204i	−0.362217	+	0.627378i	0.626108	+	0.779736i	$0.284647\pi$
$14$	0.952548	−	1.64986i	0.254579	−	0.440944i
$15$		0			0
$16$	−0.279032	−	0.483297i	−0.0697580	−	0.120824i
$17$	−0.293377			−0.0711543			−0.0355772	−	0.999367i	$-0.511327\pi$
$17$	−0.293377			−0.0711543			−0.0355772	+	0.999367i	$0.511327\pi$
$18$		0			0
$19$	−2.78475			−0.638864			−0.319432	−	0.947609i	$-0.603492\pi$
$19$	−2.78475			−0.638864			−0.319432	+	0.947609i	$0.603492\pi$
$20$	−1.86653	−	3.23292i	−0.417369	−	0.722904i
$21$		0			0
$22$	−0.100255	+	0.173646i	−0.0213743	+	0.0370214i
$23$	3.34492	−	5.79357i	0.697464	−	1.20804i	−0.271879	−	0.962332i	$-0.587645\pi$
$23$	3.34492	−	5.79357i	0.697464	−	1.20804i	0.969343	−	0.245712i	$-0.0790217\pi$
$24$		0			0
$25$	−1.28081	−	2.21843i	−0.256163	−	0.443687i
$26$	−2.09357			−0.410584
$27$		0			0
$28$	−3.22668			−0.609786
$29$	0.177529	+	0.307488i	0.0329662	+	0.0570992i	0.882038	−	0.471179i	$-0.156171\pi$
$29$	0.177529	+	0.307488i	0.0329662	+	0.0570992i	−0.849072	+	0.528278i	$0.822838\pi$
$30$		0			0
$31$	−1.38273	+	2.39496i	−0.248346	+	0.430148i	−0.963067	−	0.269262i	$-0.913220\pi$
$31$	−1.38273	+	2.39496i	−0.248346	+	0.430148i	0.714721	+	0.699410i	$0.246554\pi$
$32$	2.91482	−	5.04862i	0.515273	−	0.892478i
$33$		0			0
$34$	−0.117575	−	0.203645i	−0.0201639	−	0.0349249i
$35$	−6.53592			−1.10477
$36$		0			0
$37$	−6.99238			−1.14954			−0.574770	−	0.818315i	$-0.694909\pi$
$37$	−6.99238			−1.14954			−0.574770	+	0.818315i	$0.694909\pi$
$38$	−1.11602	−	1.93301i	−0.181043	−	0.313576i
$39$		0			0
$40$	3.70015	−	6.40884i	0.585044	−	1.01333i
$41$	4.85880	−	8.41569i	0.758818	−	1.31431i	−0.184636	−	0.982807i	$-0.559111\pi$
$41$	4.85880	−	8.41569i	0.758818	−	1.31431i	0.943454	−	0.331504i	$-0.107556\pi$
$42$		0			0
$43$	−0.130353	−	0.225778i	−0.0198787	−	0.0344309i	0.855915	−	0.517117i	$-0.172995\pi$
$43$	−0.130353	−	0.225778i	−0.0198787	−	0.0344309i	−0.875794	+	0.482686i	$0.839661\pi$
$44$	0.339604			0.0511973
$45$		0			0
$46$	5.36209			0.790597
$47$	5.71278	+	9.89482i	0.833295	+	1.44331i	0.895411	+	0.445240i	$0.146881\pi$
$47$	5.71278	+	9.89482i	0.833295	+	1.44331i	−0.0621170	+	0.998069i	$0.519785\pi$
$48$		0			0
$49$	0.675331	−	1.16971i	0.0964758	−	0.167101i
$50$	1.02661	−	1.77813i	0.145184	−	0.251466i
$51$		0			0
$52$	1.77295	+	3.07085i	0.245865	+	0.425850i
$53$	5.43137			0.746056			0.373028	−	0.927820i	$-0.378320\pi$
$53$	5.43137			0.746056			0.373028	+	0.927820i	$0.378320\pi$
$54$		0			0
$55$	0.687897			0.0927560
$56$	−3.19823	−	5.53950i	−0.427382	−	0.740247i
$57$		0			0
$58$	−0.142294	+	0.246460i	−0.0186841	+	0.0323618i
$59$	−2.98846	+	5.17617i	−0.389065	+	0.673880i	−0.992324	−	0.123665i	$-0.960535\pi$
$59$	−2.98846	+	5.17617i	−0.389065	+	0.673880i	0.603259	+	0.797545i	$0.293868\pi$
$60$		0			0
$61$	5.92338	+	10.2596i	0.758411	+	1.31361i	0.943661	+	0.330915i	$0.107357\pi$
$61$	5.92338	+	10.2596i	0.758411	+	1.31361i	−0.185249	+	0.982692i	$0.559309\pi$
$62$	−2.21660			−0.281508
$63$		0			0
$64$	3.55649			0.444561
$65$	3.59127	+	6.22026i	0.445442	+	0.771528i
$66$		0			0
$67$	−0.905151	+	1.56777i	−0.110582	+	0.191533i	−0.916005	−	0.401167i	$-0.868605\pi$
$67$	−0.905151	+	1.56777i	−0.110582	+	0.191533i	0.805423	+	0.592700i	$0.201938\pi$
$68$	−0.199138	+	0.344916i	−0.0241490	+	0.0418272i
$69$		0			0
$70$	−2.61936	−	4.53686i	−0.313073	−	0.542258i
$71$	−0.370510			−0.0439714			−0.0219857	−	0.999758i	$-0.506999\pi$
$71$	−0.370510			−0.0439714			−0.0219857	+	0.999758i	$0.506999\pi$
$72$		0			0
$73$	5.02679			0.588341			0.294171	−	0.955753i	$-0.404957\pi$
$73$	5.02679			0.588341			0.294171	+	0.955753i	$0.404957\pi$
$74$	−2.80229	−	4.85371i	−0.325760	−	0.564232i
$75$		0			0
$76$	−1.89022	+	3.27396i	−0.216823	+	0.375549i
$77$	0.297293	−	0.514927i	0.0338797	−	0.0586813i
$78$		0			0
$79$	−0.401411	−	0.695264i	−0.0451622	−	0.0782233i	0.842561	−	0.538601i	$-0.181047\pi$
$79$	−0.401411	−	0.695264i	−0.0451622	−	0.0782233i	−0.887723	+	0.460378i	$0.847714\pi$
$80$	−1.53459			−0.171572
$81$		0			0
$82$	7.78892			0.860143
$83$	1.37783	+	2.38646i	0.151236	+	0.261948i	0.931682	−	0.363275i	$-0.118341\pi$
$83$	1.37783	+	2.38646i	0.151236	+	0.261948i	−0.780446	+	0.625223i	$0.785008\pi$
$84$		0			0
$85$	−0.403370	+	0.698657i	−0.0437516	+	0.0757800i
$86$	0.104482	−	0.180967i	0.0112665	−	0.0195142i
$87$		0			0
$88$	0.336610	+	0.583026i	0.0358828	+	0.0621508i
$89$	10.4507			1.10777			0.553884	−	0.832594i	$-0.313145\pi$
$89$	10.4507			1.10777			0.553884	+	0.832594i	$0.313145\pi$
$90$		0			0
$91$	6.20825			0.650801
$92$	−4.54091	−	7.86509i	−0.473423	−	0.819992i
$93$		0			0
$94$	−4.57895	+	7.93097i	−0.472282	+	0.818017i
$95$	−3.82880	+	6.63168i	−0.392827	+	0.680396i
$96$		0			0
$97$	7.41730	+	12.8471i	0.753113	+	1.30443i	0.946307	+	0.323269i	$0.104782\pi$
$97$	7.41730	+	12.8471i	0.753113	+	1.30443i	−0.193194	+	0.981161i	$0.561885\pi$
$98$	1.08259			0.109358
$99$		0			0
$100$	−3.47755			−0.347755
$101$	−2.00266	−	3.46872i	−0.199272	−	0.345150i	0.749020	−	0.662547i	$-0.230525\pi$
$101$	−2.00266	−	3.46872i	−0.199272	−	0.345150i	−0.948293	+	0.317397i	$0.897191\pi$
$102$		0			0
$103$	2.95968	−	5.12632i	0.291626	−	0.505111i	−0.682568	−	0.730822i	$-0.739137\pi$
$103$	2.95968	−	5.12632i	0.291626	−	0.505111i	0.974194	+	0.225711i	$0.0724704\pi$
$104$	−3.51465	+	6.08755i	−0.344639	+	0.596933i
$105$		0			0
$106$	2.17669	+	3.77014i	0.211419	+	0.366189i
$107$	−0.258978			−0.0250364			−0.0125182	−	0.999922i	$-0.503985\pi$
$107$	−0.258978			−0.0250364			−0.0125182	+	0.999922i	$0.503985\pi$
$108$		0			0
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$	0.275684	+	0.477499i	0.0262854	+	0.0455277i
$111$		0			0
$112$	−0.663212	+	1.14872i	−0.0626677	+	0.108544i
$113$	1.55959	−	2.70129i	0.146714	−	0.254116i	−0.783297	−	0.621647i	$-0.786464\pi$
$113$	1.55959	−	2.70129i	0.146714	−	0.254116i	0.930011	+	0.367532i	$0.119797\pi$
$114$		0			0
$115$	−9.19800	−	15.9314i	−0.857718	−	1.48561i
$116$	0.482009			0.0447534
$117$		0			0
$118$	−4.79067			−0.441017
$119$	0.348654	+	0.603886i	0.0319611	+	0.0553582i
$120$		0			0
$121$	5.46871	−	9.47208i	0.497155	−	0.861099i
$122$	−4.74775	+	8.22334i	−0.429841	+	0.744506i
$123$		0			0
$124$	1.87714	+	3.25129i	0.168572	+	0.291975i
$125$	6.70514			0.599726
$126$		0			0
$127$	−18.4545			−1.63757			−0.818787	−	0.574097i	$-0.805353\pi$
$127$	−18.4545			−1.63757			−0.818787	+	0.574097i	$0.805353\pi$
$128$	−4.40433	−	7.62853i	−0.389292	−	0.674273i
$129$		0			0
$130$	−2.87850	+	4.98571i	−0.252461	+	0.437275i
$131$	−7.11274	+	12.3196i	−0.621443	+	1.07637i	0.367775	+	0.929915i	$0.380120\pi$
$131$	−7.11274	+	12.3196i	−0.621443	+	1.07637i	−0.989217	+	0.146455i	$0.953214\pi$
$132$		0			0
$133$	3.30944	+	5.73212i	0.286965	+	0.497037i
$134$	−1.45101			−0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	9.84279	+	17.0482i	0.840926	+	1.45653i	0.889112	+	0.457689i	$0.151323\pi$
$137$	9.84279	+	17.0482i	0.840926	+	1.45653i	−0.0481859	+	0.998838i	$0.515344\pi$
$138$		0			0
$139$	8.95548	−	15.5113i	0.759594	−	1.31565i	−0.183464	−	0.983026i	$-0.558731\pi$
$139$	8.95548	−	15.5113i	0.759594	−	1.31565i	0.943058	−	0.332629i	$-0.107936\pi$
$140$	−4.43643	+	7.68412i	−0.374947	+	0.649427i
$141$		0			0
$142$	−0.148487	−	0.257187i	−0.0124607	−	0.0215826i
$143$	−0.653411			−0.0546410
$144$		0			0
$145$	0.976351			0.0810815
$146$	2.01455	+	3.48931i	0.166726	+	0.288777i
$147$		0			0
$148$	−4.74627	+	8.22078i	−0.390141	+	0.675744i
$149$	−8.14473	+	14.1071i	−0.667242	+	1.15570i	0.311430	+	0.950269i	$0.399192\pi$
$149$	−8.14473	+	14.1071i	−0.667242	+	1.15570i	−0.978672	+	0.205428i	$0.934141\pi$
$150$		0			0
$151$	−7.13743	−	12.3624i	−0.580836	−	1.00604i	−0.995381	−	0.0960086i	$-0.969392\pi$
$151$	−7.13743	−	12.3624i	−0.580836	−	1.00604i	0.414544	−	0.910029i	$-0.363941\pi$
$152$	−7.49422			−0.607862
$153$		0			0
$154$	0.476577			0.0384036
$155$	3.80230	+	6.58577i	0.305408	+	0.528982i
$156$		0			0
$157$	−0.381677	+	0.661084i	−0.0304612	+	0.0527603i	−0.880854	−	0.473388i	$-0.843031\pi$
$157$	−0.381677	+	0.661084i	−0.0304612	+	0.0527603i	0.850393	+	0.526148i	$0.176364\pi$
$158$	0.321742	−	0.557273i	0.0255964	−	0.0443342i
$159$		0			0
$160$	−8.01530	−	13.8829i	−0.633665	−	1.09754i
$161$	−15.9006			−1.25315
$162$		0			0
$163$	5.12834			0.401682			0.200841	−	0.979624i	$-0.435632\pi$
$163$	5.12834			0.401682			0.200841	+	0.979624i	$0.435632\pi$
$164$	−6.59609	−	11.4248i	−0.515068	−	0.892124i
$165$		0			0
$166$	−1.10436	+	1.91282i	−0.0857153	+	0.148463i
$167$	−4.45056	+	7.70860i	−0.344395	+	0.596509i	−0.985244	−	0.171158i	$-0.945249\pi$
$167$	−4.45056	+	7.70860i	−0.344395	+	0.596509i	0.640849	+	0.767667i	$0.278583\pi$
$168$		0			0
$169$	3.08877	+	5.34991i	0.237598	+	0.411532i
$170$	−0.646624			−0.0495938
$171$		0			0
$172$	−0.353923			−0.0269864
$173$	3.40562	+	5.89870i	0.258924	+	0.448470i	0.965954	−	0.258714i	$-0.0832986\pi$
$173$	3.40562	+	5.89870i	0.258924	+	0.448470i	−0.707030	+	0.707184i	$0.749965\pi$
$174$		0			0
$175$	−3.04428	+	5.27285i	−0.230126	+	0.398590i
$176$	0.0698023	−	0.120901i	0.00526155	−	0.00911326i
$177$		0			0
$178$	4.18825	+	7.25425i	0.313922	+	0.543729i
$179$	−18.3476			−1.37137			−0.685684	−	0.727900i	$-0.740497\pi$
$179$	−18.3476			−1.37137			−0.685684	+	0.727900i	$0.740497\pi$
$180$		0			0
$181$	11.3256			0.841829			0.420914	−	0.907100i	$-0.361709\pi$
$181$	11.3256			0.841829			0.420914	+	0.907100i	$0.361709\pi$
$182$	2.48804	+	4.30941i	0.184426	+	0.319435i
$183$		0			0
$184$	9.00175	−	15.5915i	0.663618	−	1.14942i
$185$	−9.61397	+	16.6519i	−0.706833	+	1.22427i
$186$		0			0
$187$	−0.0366954	−	0.0635583i	−0.00268343	−	0.00464784i
$188$	15.5108			1.13124
$189$		0			0
$190$	−6.13778			−0.445281
$191$	−3.42921	−	5.93956i	−0.248129	−	0.429771i	0.714878	−	0.699249i	$-0.246482\pi$
$191$	−3.42921	−	5.93956i	−0.248129	−	0.429771i	−0.963007	+	0.269478i	$0.913149\pi$
$192$		0			0
$193$	−10.2064	+	17.6780i	−0.734673	+	1.27249i	0.220194	+	0.975456i	$0.429331\pi$
$193$	−10.2064	+	17.6780i	−0.734673	+	1.27249i	−0.954867	+	0.297034i	$0.904002\pi$
$194$	−5.94517	+	10.2973i	−0.426838	+	0.739305i
$195$		0			0
$196$	−0.916798	−	1.58794i	−0.0654856	−	0.113424i
$197$	3.03573			0.216287			0.108143	−	0.994135i	$-0.465509\pi$
$197$	3.03573			0.216287			0.108143	+	0.994135i	$0.465509\pi$
$198$		0			0
$199$	−2.26247			−0.160382			−0.0801912	−	0.996779i	$-0.525553\pi$
$199$	−2.26247			−0.160382			−0.0801912	+	0.996779i	$0.525553\pi$
$200$	−3.44689	−	5.97018i	−0.243732	−	0.422156i
$201$		0			0
$202$	1.60519	−	2.78027i	0.112941	−	0.195619i
$203$	0.421956	−	0.730849i	0.0296155	−	0.0512955i
$204$		0			0
$205$	−13.3609	−	23.1418i	−0.933168	−	1.61629i
$206$	4.74453			0.330567
$207$		0			0
$208$	1.45765			0.101070
$209$	−0.348314	−	0.603298i	−0.0240934	−	0.0417310i
$210$		0			0
$211$	−12.7154	+	22.0237i	−0.875364	+	1.51618i	−0.0189904	+	0.999820i	$0.506045\pi$
$211$	−12.7154	+	22.0237i	−0.875364	+	1.51618i	−0.856374	+	0.516356i	$0.827288\pi$
$212$	3.68669	−	6.38553i	0.253203	−	0.438560i
$213$		0			0
$214$	−0.103789	−	0.179768i	−0.00709488	−	0.0122887i
$215$	−0.716901			−0.0488923
$216$		0			0
$217$	6.57305			0.446208
$218$	−3.42968	−	5.94038i	−0.232287	−	0.402334i
$219$		0			0
$220$	0.466929	−	0.808745i	0.0314803	−	0.0545256i
$221$	0.383148	−	0.663631i	0.0257733	−	0.0446407i
$222$		0			0
$223$	1.91567	+	3.31804i	0.128283	+	0.222192i	0.923011	−	0.384773i	$-0.125720\pi$
$223$	1.91567	+	3.31804i	0.128283	+	0.222192i	−0.794729	+	0.606965i	$0.792387\pi$
$224$	−13.8561			−0.925799
$225$		0			0
$226$	2.50011			0.166305
$227$	−1.25800	−	2.17891i	−0.0834961	−	0.144619i	0.821253	−	0.570564i	$-0.193275\pi$
$227$	−1.25800	−	2.17891i	−0.0834961	−	0.144619i	−0.904749	+	0.425944i	$0.859942\pi$
$228$		0			0
$229$	7.96981	−	13.8041i	0.526660	−	0.912202i	−0.472858	−	0.881139i	$-0.656777\pi$
$229$	7.96981	−	13.8041i	0.526660	−	0.912202i	0.999517	−	0.0310628i	$-0.00988918\pi$
$230$	7.37245	−	12.7694i	0.486125	−	0.841993i
$231$		0			0
$232$	0.477760	+	0.827504i	0.0313665	+	0.0543283i
$233$	28.1283			1.84274			0.921372	−	0.388682i	$-0.127070\pi$
$233$	28.1283			1.84274			0.921372	+	0.388682i	$0.127070\pi$
$234$		0			0
$235$	31.4185			2.04952
$236$	4.05700	+	7.02693i	0.264088	+	0.457414i
$237$		0			0
$238$	−0.279456	+	0.484031i	−0.0181144	+	0.0313751i
$239$	7.35289	−	12.7356i	0.475619	−	0.823797i	−0.523991	−	0.851724i	$-0.675557\pi$
$239$	7.35289	−	12.7356i	0.475619	−	0.823797i	0.999610	+	0.0279273i	$0.00889069\pi$
$240$		0			0
$241$	−4.22147	−	7.31181i	−0.271929	−	0.470995i	0.697427	−	0.716656i	$-0.254328\pi$
$241$	−4.22147	−	7.31181i	−0.271929	−	0.470995i	−0.969356	+	0.245661i	$0.920995\pi$
$242$	8.76664			0.563541
$243$		0			0
$244$	16.0826			1.02958
$245$	−1.85705	−	3.21651i	−0.118643	−	0.205495i
$246$		0			0
$247$	3.63685	−	6.29922i	0.231407	−	0.400809i
$248$	−3.72117	+	6.44526i	−0.236295	+	0.409274i
$249$		0			0
$250$	2.68718	+	4.65432i	0.169952	+	0.294365i
$251$	−23.2205			−1.46566			−0.732832	−	0.680409i	$-0.761802\pi$
$251$	−23.2205			−1.46566			−0.732832	+	0.680409i	$0.761802\pi$
$252$		0			0
$253$	1.67352			0.105213
$254$	−7.39590	−	12.8101i	−0.464060	−	0.803775i
$255$		0			0
$256$	7.08668	−	12.2745i	0.442918	−	0.767156i
$257$	−3.43260	+	5.94544i	−0.214120	+	0.370866i	−0.953000	−	0.302971i	$-0.902022\pi$
$257$	−3.43260	+	5.94544i	−0.214120	+	0.370866i	0.738880	+	0.673837i	$0.235355\pi$
$258$		0			0
$259$	8.30986	+	14.3931i	0.516350	+	0.894344i
$260$	9.75069			0.604712
$261$		0			0
$262$	−11.4021			−0.704424
$263$	−1.67647	−	2.90373i	−0.103376	−	0.179052i	0.809698	−	0.586847i	$-0.199631\pi$
$263$	−1.67647	−	2.90373i	−0.103376	−	0.179052i	−0.913073	+	0.407795i	$0.866298\pi$
$264$		0			0
$265$	7.46770	−	12.9344i	0.458737	−	0.794556i
$266$	−2.65260	+	4.59444i	−0.162642	+	0.281703i
$267$		0			0
$268$	1.22879	+	2.12833i	0.0750604	+	0.130008i
$269$	12.7416			0.776869			0.388434	−	0.921476i	$-0.373016\pi$
$269$	12.7416			0.776869			0.388434	+	0.921476i	$0.373016\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	0.0818615	+	0.141788i	0.00496358	+	0.00859717i
$273$		0			0
$274$	−7.88926	+	13.6646i	−0.476608	+	0.825509i
$275$	0.320407	−	0.554961i	0.0193213	−	0.0334654i
$276$		0			0
$277$	−2.09061	−	3.62104i	−0.125613	−	0.217567i	0.796360	−	0.604823i	$-0.206756\pi$
$277$	−2.09061	−	3.62104i	−0.125613	−	0.217567i	−0.921972	+	0.387256i	$0.873423\pi$
$278$	14.3561			0.861023
$279$		0			0
$280$	−17.5893			−1.05116
$281$	10.8180	+	18.7373i	0.645348	+	1.11778i	0.984221	+	0.176944i	$0.0566211\pi$
$281$	10.8180	+	18.7373i	0.645348	+	1.11778i	−0.338873	+	0.940832i	$0.610046\pi$
$282$		0			0
$283$	−2.61367	+	4.52701i	−0.155366	+	0.269103i	−0.933192	−	0.359377i	$-0.882989\pi$
$283$	−2.61367	+	4.52701i	−0.155366	+	0.269103i	0.777826	+	0.628480i	$0.216323\pi$
$284$	−0.251494	+	0.435600i	−0.0149234	+	0.0258481i
$285$		0			0
$286$	−0.261863	−	0.453560i	−0.0154843	−	0.0268196i
$287$	−23.0971			−1.36338
$288$		0			0
$289$	−16.9139			−0.994937
$290$	0.391286	+	0.677727i	0.0229771	+	0.0397975i
$291$		0			0
$292$	3.41207	−	5.90988i	0.199676	−	0.345849i
$293$	3.07108	−	5.31927i	0.179415	−	0.310755i	−0.762266	−	0.647264i	$-0.775913\pi$
$293$	3.07108	−	5.31927i	0.179415	−	0.310755i	0.941680	+	0.336509i	$0.109246\pi$
$294$		0			0
$295$	8.21780	+	14.2336i	0.478459	+	0.828715i
$296$	−18.8177			−1.09376
$297$		0			0
$298$	−13.0564			−0.756339
$299$	8.73688	+	15.1327i	0.505267	+	0.875147i
$300$		0			0
$301$	−0.309828	+	0.536638i	−0.0178582	+	0.0309313i
$302$	5.72085	−	9.90879i	0.329198	−	0.570187i
$303$		0			0
$304$	0.777033	+	1.34586i	0.0445659	+	0.0771904i
$305$	32.5767			1.86534
$306$		0			0
$307$	19.0039			1.08461			0.542304	−	0.840182i	$-0.317552\pi$
$307$	19.0039			1.08461			0.542304	+	0.840182i	$0.317552\pi$
$308$	−0.403591	−	0.699041i	−0.0229968	−	0.0398316i
$309$		0			0
$310$	−3.04764	+	5.27867i	−0.173094	+	0.299808i
$311$	10.7735	−	18.6602i	0.610907	−	1.05812i	−0.380181	−	0.924912i	$-0.624138\pi$
$311$	10.7735	−	18.6602i	0.610907	−	1.05812i	0.991088	−	0.133209i	$-0.0425283\pi$
$312$		0			0
$313$	1.90681	+	3.30269i	0.107779	+	0.186679i	0.914870	−	0.403748i	$-0.132293\pi$
$313$	1.90681	+	3.30269i	0.107779	+	0.186679i	−0.807091	+	0.590427i	$0.798959\pi$
$314$	−0.611849			−0.0345286
$315$		0			0
$316$	−1.08987			−0.0613102
$317$	−2.12724	−	3.68449i	−0.119478	−	0.206942i	0.800083	−	0.599889i	$-0.204789\pi$
$317$	−2.12724	−	3.68449i	−0.119478	−	0.206942i	−0.919561	+	0.392948i	$0.871455\pi$
$318$		0			0
$319$	−0.0444103	+	0.0769210i	−0.00248650	+	0.00430675i
$320$	4.88989	−	8.46954i	0.273353	−	0.473462i
$321$		0			0
$322$	−6.37240	−	11.0373i	−0.355120	−	0.615085i
$323$	0.816980			0.0454580
$324$		0			0
$325$	6.69092			0.371146
$326$	2.05525	+	3.55980i	0.113830	+	0.197159i
$327$		0			0
$328$	13.0759	−	22.6481i	0.721994	−	1.25053i
$329$	13.5783	−	23.5184i	0.748597	−	1.29661i
$330$		0			0
$331$	7.14690	+	12.3788i	0.392829	+	0.680400i	0.992821	−	0.119606i	$-0.0381631\pi$
$331$	7.14690	+	12.3788i	0.392829	+	0.680400i	−0.599993	+	0.800006i	$0.704830\pi$
$332$	3.74095			0.205311
$333$		0			0
$334$	−7.13449			−0.390382
$335$	2.48902	+	4.31111i	0.135990	+	0.235541i
$336$		0			0
$337$	−17.8593	+	30.9331i	−0.972855	+	1.68503i	−0.286017	+	0.958224i	$0.592331\pi$
$337$	−17.8593	+	30.9331i	−0.972855	+	1.68503i	−0.686838	+	0.726810i	$0.741002\pi$
$338$	−2.47573	+	4.28810i	−0.134662	+	0.233242i
$339$		0			0
$340$	0.547597	+	0.948465i	0.0296976	+	0.0514377i
$341$	−0.691806			−0.0374634
$342$		0			0
$343$	−19.8481			−1.07170
$344$	−0.350803	−	0.607608i	−0.0189140	−	0.0327600i
$345$		0			0
$346$	−2.72970	+	4.72797i	−0.146749	+	0.254177i
$347$	9.72077	−	16.8369i	0.521838	−	0.903850i	−0.477839	−	0.878447i	$-0.658580\pi$
$347$	9.72077	−	16.8369i	0.521838	−	0.903850i	0.999677	−	0.0254027i	$-0.00808679\pi$
$348$		0			0
$349$	4.01035	+	6.94613i	0.214669	+	0.371818i	0.953170	−	0.302434i	$-0.0977993\pi$
$349$	4.01035	+	6.94613i	0.214669	+	0.371818i	−0.738501	+	0.674252i	$0.764466\pi$
$350$	−4.88014			−0.260855
$351$		0			0
$352$	1.45834			0.0777296
$353$	−4.37691	−	7.58103i	−0.232959	−	0.403497i	0.725718	−	0.687992i	$-0.241508\pi$
$353$	−4.37691	−	7.58103i	−0.232959	−	0.403497i	−0.958678	+	0.284495i	$0.908174\pi$
$354$		0			0
$355$	−0.509422	+	0.882344i	−0.0270373	+	0.0468300i
$356$	7.09367	−	12.2866i	0.375964	−	0.651189i
$357$		0			0
$358$	−7.35307	−	12.7359i	−0.388622	−	0.673112i
$359$	−8.27791			−0.436892			−0.218446	−	0.975849i	$-0.570099\pi$
$359$	−8.27791			−0.436892			−0.218446	+	0.975849i	$0.570099\pi$
$360$		0			0
$361$	−11.2452			−0.591852
$362$	4.53891	+	7.86162i	0.238560	+	0.413197i
$363$		0			0
$364$	4.21402	−	7.29890i	0.220875	−	0.382566i
$365$	6.91143	−	11.9710i	0.361761	−	0.626588i
$366$		0			0
$367$	7.39993	+	12.8171i	0.386273	+	0.669045i	0.991945	−	0.126670i	$-0.0404289\pi$
$367$	7.39993	+	12.8171i	0.386273	+	0.669045i	−0.605672	+	0.795715i	$0.707096\pi$
$368$	−3.73336			−0.194615
$369$		0			0
$370$	−15.4117			−0.801216
$371$	−6.45473	−	11.1799i	−0.335113	−	0.580433i
$372$		0			0
$373$	−12.7667	+	22.1126i	−0.661035	+	1.14495i	0.319310	+	0.947650i	$0.396549\pi$
$373$	−12.7667	+	22.1126i	−0.661035	+	1.14495i	−0.980344	+	0.197295i	$0.936784\pi$
$374$	0.0294124	−	0.0509437i	0.00152088	−	0.00263424i
$375$		0			0
$376$	15.3741	+	26.6287i	0.792857	+	1.37327i
$377$	−0.927403			−0.0477637
$378$		0			0
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$	5.19781	+	9.00287i	0.266642	+	0.461838i
$381$		0			0
$382$	2.74860	−	4.76072i	0.140631	−	0.243579i
$383$	11.9306	−	20.6645i	0.609627	−	1.05590i	−0.381675	−	0.924296i	$-0.624653\pi$
$383$	11.9306	−	20.6645i	0.609627	−	1.05590i	0.991302	−	0.131608i	$-0.0420139\pi$
$384$		0			0
$385$	−0.817509	−	1.41597i	−0.0416641	−	0.0721643i
$386$	−16.3614			−0.832774
$387$		0			0
$388$	20.1388			1.02239
$389$	−18.9867	−	32.8858i	−0.962662	−	1.66738i	−0.715771	−	0.698335i	$-0.753924\pi$
$389$	−18.9867	−	32.8858i	−0.962662	−	1.66738i	−0.246891	−	0.969043i	$-0.579409\pi$
$390$		0			0
$391$	−0.981322	+	1.69970i	−0.0496276	+	0.0859575i
$392$	1.81743	−	3.14788i	0.0917941	−	0.158992i
$393$		0			0
$394$	1.21661	+	2.10723i	0.0612919	+	0.106161i
$395$	−2.20763			−0.111078
$396$		0			0
$397$	20.3493			1.02130			0.510651	−	0.859788i	$-0.329404\pi$
$397$	20.3493			1.02130			0.510651	+	0.859788i	$0.329404\pi$
$398$	−0.906716	−	1.57048i	−0.0454496	−	0.0787210i
$399$		0			0
$400$	−0.714775	+	1.23803i	−0.0357388	+	0.0619014i
$401$	−3.47248	+	6.01452i	−0.173408	+	0.300351i	−0.939609	−	0.342250i	$-0.888811\pi$
$401$	−3.47248	+	6.01452i	−0.173408	+	0.300351i	0.766201	+	0.642600i	$0.222144\pi$
$402$		0			0
$403$	−3.61168	−	6.25561i	−0.179910	−	0.311614i
$404$	−5.43745			−0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	−0.874603	−	1.51486i	−0.0433525	−	0.0750887i
$408$		0			0
$409$	5.45298	−	9.44483i	0.269632	−	0.467017i	−0.699135	−	0.714990i	$-0.746431\pi$
$409$	5.45298	−	9.44483i	0.269632	−	0.467017i	0.968767	+	0.247973i	$0.0797645\pi$
$410$	10.7092	−	18.5488i	0.528887	−	0.916060i
$411$		0			0
$412$	−4.01793	−	6.95925i	−0.197949	−	0.342858i
$413$	14.2062			0.699040
$414$		0			0
$415$	7.57760			0.371970
$416$	7.61347	+	13.1869i	0.373281	+	0.646541i
$417$		0			0
$418$	0.279183	−	0.483560i	0.0136553	−	0.0236517i
$419$	5.03459	−	8.72017i	0.245956	−	0.426008i	−0.716444	−	0.697645i	$-0.754231\pi$
$419$	5.03459	−	8.72017i	0.245956	−	0.426008i	0.962400	+	0.271636i	$0.0875648\pi$
$420$		0			0
$421$	1.55378	+	2.69123i	0.0757267	+	0.131163i	0.901402	−	0.432983i	$-0.142539\pi$
$421$	1.55378	+	2.69123i	0.0757267	+	0.131163i	−0.825675	+	0.564146i	$0.809206\pi$
$422$	−20.3835			−0.992252
$423$		0			0
$424$	14.6167			0.709852
$425$	0.375761	+	0.650837i	0.0182271	+	0.0315702i
$426$		0			0
$427$	14.0789	−	24.3854i	0.681325	−	1.18009i
$428$	−0.175789	+	0.304475i	−0.00849707	+	0.0147174i
$429$		0			0
$430$	−0.287308	−	0.497632i	−0.0138552	−	0.0239979i
$431$	−28.0701			−1.35209			−0.676044	−	0.736862i	$-0.736307\pi$
$431$	−28.0701			−1.35209			−0.676044	+	0.736862i	$0.736307\pi$
$432$		0			0
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$	2.63424	+	4.56264i	0.126448	+	0.219014i
$435$		0			0
$436$	−5.80889	+	10.0613i	−0.278195	+	0.481848i
$437$	−9.31475	+	16.1336i	−0.445585	+	0.771776i
$438$		0			0
$439$	−7.31479	−	12.6696i	−0.349116	−	0.604686i	0.636977	−	0.770883i	$-0.280185\pi$
$439$	−7.31479	−	12.6696i	−0.349116	−	0.604686i	−0.986093	+	0.166197i	$0.946851\pi$
$440$	1.85125			0.0882548
$441$		0			0
$442$	0.614206			0.0292148
$443$	−9.17797	−	15.8967i	−0.436059	−	0.755276i	0.561323	−	0.827597i	$-0.310293\pi$
$443$	−9.17797	−	15.8967i	−0.436059	−	0.755276i	−0.997381	+	0.0723212i	$0.976959\pi$
$444$		0			0
$445$	14.3688	−	24.8876i	0.681148	−	1.17978i
$446$	−1.53546	+	2.65950i	−0.0727061	+	0.125931i
$447$		0			0
$448$	−4.22659	−	7.32067i	−0.199688	−	0.345869i
$449$	13.8594			0.654065			0.327032	−	0.945013i	$-0.393951\pi$
$449$	13.8594			0.654065			0.327032	+	0.945013i	$0.393951\pi$
$450$		0			0
$451$	2.43095			0.114469
$452$	−2.11723	−	3.66715i	−0.0995860	−	0.172488i
$453$		0			0
$454$	1.00832	−	1.74646i	0.0473227	−	0.0819653i
$455$	8.53585	−	14.7845i	0.400167	−	0.693109i
$456$		0			0
$457$	−8.82406	−	15.2837i	−0.412772	−	0.714943i	0.582419	−	0.812888i	$-0.302106\pi$
$457$	−8.82406	−	15.2837i	−0.412772	−	0.714943i	−0.995192	+	0.0979458i	$0.968773\pi$
$458$	12.7760			0.596985
$459$		0			0
$460$	−24.9736			−1.16440
$461$	−12.8190	−	22.2032i	−0.597041	−	1.03411i	−0.993255	−	0.115947i	$-0.963010\pi$
$461$	−12.8190	−	22.2032i	−0.597041	−	1.03411i	0.396214	−	0.918158i	$-0.370324\pi$
$462$		0			0
$463$	−9.17371	+	15.8893i	−0.426339	+	0.738440i	−0.996544	−	0.0830618i	$-0.973530\pi$
$463$	−9.17371	+	15.8893i	−0.426339	+	0.738440i	0.570206	+	0.821502i	$0.306863\pi$
$464$	0.0990722	−	0.171598i	0.00459931	−	0.00796624i
$465$		0			0
$466$	11.2728	+	19.5250i	0.522201	+	0.904479i
$467$	−16.2618			−0.752509			−0.376254	−	0.926516i	$-0.622788\pi$
$467$	−16.2618			−0.752509			−0.376254	+	0.926516i	$0.622788\pi$
$468$		0			0
$469$	4.30279			0.198684
$470$	12.5914	+	21.8089i	0.580797	+	1.00597i
$471$		0			0
$472$	−8.04246	+	13.9300i	−0.370184	+	0.641178i
$473$	0.0326090	−	0.0564805i	0.00149936	−	0.00259697i
$474$		0			0
$475$	3.56674	+	6.17777i	0.163653	+	0.283456i
$476$	0.946634			0.0433889
$477$		0			0
$478$	11.7871			0.539129
$479$	4.73585	+	8.20274i	0.216387	+	0.374793i	0.953701	−	0.300757i	$-0.0972395\pi$
$479$	4.73585	+	8.20274i	0.216387	+	0.374793i	−0.737314	+	0.675550i	$0.763906\pi$
$480$		0			0
$481$	9.13199	−	15.8171i	0.416383	−	0.721196i
$482$	3.38362	−	5.86061i	0.154120	−	0.266943i
$483$		0			0
$484$	−7.42407	−	12.8589i	−0.337458	−	0.584494i
$485$	40.7928			1.85231
$486$		0			0
$487$	−0.467564			−0.0211874			−0.0105937	−	0.999944i	$-0.503372\pi$
$487$	−0.467564			−0.0211874			−0.0105937	+	0.999944i	$0.503372\pi$
$488$	15.9408	+	27.6103i	0.721607	+	1.24986i
$489$		0			0
$490$	1.48848	−	2.57812i	0.0672425	−	0.116467i
$491$	−12.5235	+	21.6913i	−0.565177	+	0.978916i	0.431856	+	0.901943i	$0.357859\pi$
$491$	−12.5235	+	21.6913i	−0.565177	+	0.978916i	−0.997033	+	0.0769733i	$0.975474\pi$
$492$		0			0
$493$	−0.0520828	−	0.0902100i	−0.00234569	−	0.00406285i
$494$	5.83007			0.262307
$495$		0			0
$496$	1.54331			0.0692965
$497$	0.440320	+	0.762657i	0.0197511	+	0.0342098i
$498$		0			0
$499$	7.01708	−	12.1539i	0.314128	−	0.544085i	−0.665124	−	0.746733i	$-0.731621\pi$
$499$	7.01708	−	12.1539i	0.314128	−	0.544085i	0.979252	+	0.202648i	$0.0649547\pi$
$500$	4.55130	−	7.88308i	0.203540	−	0.352542i
$501$		0			0
$502$	−9.30593	−	16.1183i	−0.415344	−	0.719397i
$503$	28.3116			1.26235			0.631176	−	0.775640i	$-0.282573\pi$
$503$	28.3116			1.26235			0.631176	+	0.775640i	$0.282573\pi$
$504$		0			0
$505$	−11.0140			−0.490117
$506$	0.670687	+	1.16166i	0.0298157	+	0.0516423i
$507$		0			0
$508$	−12.5265	+	21.6966i	−0.555774	+	0.962629i
$509$	14.3437	−	24.8441i	0.635774	−	1.10119i	−0.350576	−	0.936534i	$-0.614014\pi$
$509$	14.3437	−	24.8441i	0.635774	−	1.10119i	0.986350	−	0.164659i	$-0.0526525\pi$
$510$		0			0
$511$	−5.97392	−	10.3471i	−0.264271	−	0.457730i
$512$	−6.25700			−0.276523
$513$		0			0
$514$	−5.50264			−0.242711
$515$	−8.13865	−	14.0966i	−0.358632	−	0.621168i
$516$		0			0
$517$	−1.42910	+	2.47528i	−0.0628519	+	0.108863i
$518$	−6.66058	+	11.5365i	−0.292649	+	0.506883i
$519$		0			0
$520$	9.66472	+	16.7398i	0.423826	+	0.734088i
$521$	−24.9096			−1.09131			−0.545655	−	0.838010i	$-0.683719\pi$
$521$	−24.9096			−1.09131			−0.545655	+	0.838010i	$0.683719\pi$
$522$		0			0
$523$	−25.8648			−1.13099			−0.565494	−	0.824753i	$-0.691314\pi$
$523$	−25.8648			−1.13099			−0.565494	+	0.824753i	$0.691314\pi$
$524$	9.65593	+	16.7246i	0.421821	+	0.730616i
$525$		0			0
$526$	1.34374	−	2.32742i	0.0585896	−	0.101480i
$527$	0.405662	−	0.702627i	0.0176709	−	0.0306069i
$528$		0			0
$529$	−10.8770	−	18.8395i	−0.472913	−	0.819109i
$530$	11.9711			0.519992
$531$		0			0
$532$	8.98549			0.389570
$533$	12.6911	+	21.9817i	0.549713	+	0.952131i
$534$		0			0
$535$	−0.356075	+	0.616740i	−0.0153945	+	0.0266640i
$536$	−2.43592	+	4.21913i	−0.105216	+	0.182239i
$537$		0			0
$538$	5.10637	+	8.84448i	0.220151	+	0.381313i
$539$	0.337880			0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	−9.44063	−	16.3516i	−0.405510	−	0.702363i
$543$		0			0
$544$	−0.855141	+	1.48115i	−0.0366639	+	0.0635037i
$545$	−11.7664	+	20.3800i	−0.504017	+	0.872983i
$546$		0			0
$547$	4.98802	+	8.63951i	0.213273	+	0.369399i	0.952737	−	0.303797i	$-0.0982544\pi$
$547$	4.98802	+	8.63951i	0.213273	+	0.369399i	−0.739464	+	0.673196i	$0.764921\pi$
$548$	26.7243			1.14160
$549$		0			0
$550$	0.513629			0.0219012
$551$	−0.494372	−	0.856277i	−0.0210609	−	0.0364786i
$552$		0			0
$553$	−0.954087	+	1.65253i	−0.0405719	+	0.0702726i
$554$	1.67568	−	2.90236i	0.0711928	−	0.123310i
$555$		0			0
$556$	−12.1576	−	21.0575i	−0.515595	−	0.893037i
$557$	−18.5330			−0.785268			−0.392634	−	0.919695i	$-0.628436\pi$
$557$	−18.5330			−0.785268			−0.392634	+	0.919695i	$0.628436\pi$
$558$		0			0
$559$	0.680961			0.0288016
$560$	1.82373	+	3.15879i	0.0770666	+	0.133483i
$561$		0			0
$562$	−8.67092	+	15.0185i	−0.365761	+	0.633516i
$563$	−21.8415	+	37.8307i	−0.920511	+	1.59437i	−0.121886	+	0.992544i	$0.538894\pi$
$563$	−21.8415	+	37.8307i	−0.920511	+	1.59437i	−0.798625	+	0.601828i	$0.794439\pi$
$564$		0			0
$565$	−4.28862	−	7.42811i	−0.180424	−	0.312503i
$566$	−4.18985			−0.176113
$567$		0			0
$568$	−0.997105			−0.0418376
$569$	−6.78334	−	11.7491i	−0.284373	−	0.492548i	0.688084	−	0.725631i	$-0.258452\pi$
$569$	−6.78334	−	11.7491i	−0.284373	−	0.492548i	−0.972457	+	0.233083i	$0.925119\pi$
$570$		0			0
$571$	−11.8744	+	20.5670i	−0.496926	+	0.860702i	−0.999994	−	0.00354552i	$-0.998871\pi$
$571$	−11.8744	+	20.5670i	−0.496926	+	0.860702i	0.503067	+	0.864247i	$0.332205\pi$
$572$	−0.443520	+	0.768200i	−0.0185445	+	0.0321200i
$573$		0			0
$574$	−9.25649	−	16.0327i	−0.386358	−	0.669192i
$575$	−17.1369			−0.714657
$576$		0			0
$577$	−8.11902			−0.337999			−0.169000	−	0.985616i	$-0.554054\pi$
$577$	−8.11902			−0.337999			−0.169000	+	0.985616i	$0.554054\pi$
$578$	−6.77849	−	11.7407i	−0.281948	−	0.488348i
$579$		0			0
$580$	0.662725	−	1.14787i	0.0275181	−	0.0476628i
$581$	3.27486	−	5.67223i	0.135864	−	0.235324i
$582$		0			0
$583$	0.679353	+	1.17667i	0.0281359	+	0.0487328i
$584$	13.5279			0.559790
$585$		0			0
$586$	4.92311			0.203372
$587$	1.84600	+	3.19736i	0.0761925	+	0.131969i	0.901604	−	0.432562i	$-0.142390\pi$
$587$	1.84600	+	3.19736i	0.0761925	+	0.131969i	−0.825412	+	0.564531i	$0.809057\pi$
$588$		0			0
$589$	3.85056	−	6.66936i	0.158660	−	0.274806i
$590$	−6.58679	+	11.4087i	−0.271174	+	0.469687i
$591$		0			0
$592$	1.95110	+	3.37940i	0.0801896	+	0.138892i
$593$	29.4590			1.20974			0.604869	−	0.796325i	$-0.293226\pi$
$593$	29.4590			1.20974			0.604869	+	0.796325i	$0.293226\pi$
$594$		0			0
$595$	1.91749			0.0786093
$596$	11.0569	+	19.1511i	0.452909	+	0.784461i
$597$		0			0
$598$	−7.00284	+	12.1293i	−0.286368	+	0.496003i
$599$	10.9377	−	18.9446i	0.446902	−	0.774057i	−0.551280	−	0.834320i	$-0.685861\pi$
$599$	10.9377	−	18.9446i	0.446902	−	0.774057i	0.998183	+	0.0602628i	$0.0191939\pi$
$600$		0			0
$601$	−18.2603	−	31.6278i	−0.744854	−	1.29013i	−0.950263	−	0.311449i	$-0.899186\pi$
$601$	−18.2603	−	31.6278i	−0.744854	−	1.29013i	0.205408	−	0.978676i	$-0.434148\pi$
$602$	−0.496671			−0.0202428
$603$		0			0
$604$	−19.3789			−0.788517
$605$	−15.0381	−	26.0467i	−0.611385	−	1.05895i
$606$		0			0
$607$	3.29041	−	5.69916i	0.133554	−	0.231322i	−0.791490	−	0.611182i	$-0.790694\pi$
$607$	3.29041	−	5.69916i	0.133554	−	0.231322i	0.925044	+	0.379860i	$0.124028\pi$
$608$	−8.11704	+	14.0591i	−0.329189	+	0.570173i
$609$		0			0
$610$	13.0556	+	22.6129i	0.528604	+	0.915569i
$611$	−29.8434			−1.20733
$612$		0			0
$613$	−7.14867			−0.288732			−0.144366	−	0.989524i	$-0.546114\pi$
$613$	−7.14867			−0.288732			−0.144366	+	0.989524i	$0.546114\pi$
$614$	7.61606	+	13.1914i	0.307359	+	0.532361i
$615$		0			0
$616$	0.800066	−	1.38576i	0.0322356	−	0.0558337i
$617$	−8.26874	+	14.3219i	−0.332887	+	0.576577i	−0.983077	−	0.183195i	$-0.941356\pi$
$617$	−8.26874	+	14.3219i	−0.332887	+	0.576577i	0.650190	+	0.759772i	$0.274689\pi$
$618$		0			0
$619$	0.749675	+	1.29848i	0.0301320	+	0.0521901i	0.880698	−	0.473678i	$-0.157074\pi$
$619$	0.749675	+	1.29848i	0.0301320	+	0.0521901i	−0.850566	+	0.525868i	$0.823741\pi$
$620$	10.3236			0.414608
$621$		0			0
$622$	17.2704			0.692481
$623$	−12.4197	−	21.5116i	−0.497587	−	0.861845i
$624$		0			0
$625$	15.6231	−	27.0600i	0.624924	−	1.08240i
$626$	−1.52836	+	2.64719i	−0.0610855	+	0.105803i
$627$		0			0
$628$	0.518148	+	0.897458i	0.0206763	+	0.0358125i
$629$	2.05140			0.0817948
$630$		0			0
$631$	−35.8913			−1.42881			−0.714404	−	0.699733i	$-0.753302\pi$
$631$	−35.8913			−1.42881			−0.714404	+	0.699733i	$0.753302\pi$
$632$	−1.08026	−	1.87107i	−0.0429706	−	0.0744273i
$633$		0			0
$634$	1.70504	−	2.95322i	0.0677159	−	0.117287i
$635$	−25.3735	+	43.9482i	−1.00692	+	1.74403i
$636$		0			0
$637$	1.76395	+	3.05525i	0.0698903	+	0.121054i
$638$	−0.0711922			−0.00281852
$639$		0			0
$640$	−24.2224			−0.957476
$641$	−19.6140	−	33.9724i	−0.774705	−	1.34183i	−0.934960	−	0.354753i	$-0.884565\pi$
$641$	−19.6140	−	33.9724i	−0.774705	−	1.34183i	0.160255	−	0.987076i	$-0.448769\pi$
$642$		0			0
$643$	5.20925	−	9.02269i	0.205433	−	0.355820i	−0.744838	−	0.667246i	$-0.767473\pi$
$643$	5.20925	−	9.02269i	0.205433	−	0.355820i	0.950271	+	0.311426i	$0.100806\pi$
$644$	−10.7930	+	18.6940i	−0.425304	+	0.736647i
$645$		0			0
$646$	0.327416	+	0.567100i	0.0128820	+	0.0223123i
$647$	−39.1517			−1.53921			−0.769606	−	0.638519i	$-0.779547\pi$
$647$	−39.1517			−1.53921			−0.769606	+	0.638519i	$0.779547\pi$
$648$		0			0
$649$	−1.49518			−0.0586910
$650$	2.68148	+	4.64446i	0.105176	+	0.182171i
$651$		0			0
$652$	3.48100	−	6.02927i	0.136326	−	0.236124i
$653$	−16.4549	+	28.5008i	−0.643932	+	1.11532i	0.340615	+	0.940203i	$0.389365\pi$
$653$	−16.4549	+	28.5008i	−0.643932	+	1.11532i	−0.984547	+	0.175120i	$0.943969\pi$
$654$		0			0
$655$	19.5589	+	33.8770i	0.764229	+	1.32368i
$656$	−5.42304			−0.211734
$657$		0			0
$658$	21.7668			0.848558
$659$	10.7842	+	18.6788i	0.420093	+	0.727623i	0.995948	−	0.0899293i	$-0.0286641\pi$
$659$	10.7842	+	18.6788i	0.420093	+	0.727623i	−0.575855	+	0.817552i	$0.695331\pi$
$660$		0			0
$661$	−13.1482	+	22.7733i	−0.511405	+	0.885780i	0.488507	+	0.872560i	$0.337541\pi$
$661$	−13.1482	+	22.7733i	−0.511405	+	0.885780i	−0.999913	+	0.0132199i	$0.995792\pi$
$662$	−5.72843	+	9.92193i	−0.222642	+	0.385627i
$663$		0			0
$664$	3.70796	+	6.42238i	0.143897	+	0.249237i
$665$	18.2009			0.705799
$666$		0			0
$667$	2.37528			0.0919710
$668$	6.04188	+	10.4648i	0.233767	+	0.404897i
$669$		0			0
$670$	−1.99502	+	3.45547i	−0.0770743	+	0.133497i
$671$	−1.48179	+	2.56653i	−0.0572037	+	0.0990797i
$672$		0			0
$673$	−5.76106	−	9.97845i	−0.222073	−	0.384641i	0.733365	−	0.679836i	$-0.237949\pi$
$673$	−5.76106	−	9.97845i	−0.222073	−	0.384641i	−0.955437	+	0.295195i	$0.904616\pi$
$674$	−28.6293			−1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	16.9625	+	29.3799i	0.651922	+	1.12916i	0.982656	+	0.185438i	$0.0593704\pi$
$677$	16.9625	+	29.3799i	0.651922	+	1.12916i	−0.330734	+	0.943724i	$0.607296\pi$
$678$		0			0
$679$	17.6297	−	30.5355i	0.676566	−	1.17185i
$680$	−1.08554	+	1.88021i	−0.0416284	+	0.0721026i
$681$		0			0
$682$	−0.277251	−	0.480212i	−0.0106165	−	0.0183883i
$683$	36.7553			1.40640			0.703201	−	0.710991i	$-0.251753\pi$
$683$	36.7553			1.40640			0.703201	+	0.710991i	$0.251753\pi$
$684$		0			0
$685$	54.1322			2.06829
$686$	−7.95441	−	13.7774i	−0.303701	−	0.526025i
$687$		0			0
$688$	−0.0727454	+	0.125999i	−0.00277339	+	0.00480366i
$689$	−7.09332	+	12.2860i	−0.270234	+	0.468059i
$690$		0			0
$691$	−6.68906	−	11.5858i	−0.254464	−	0.440744i	0.710286	−	0.703913i	$-0.248566\pi$
$691$	−6.68906	−	11.5858i	−0.254464	−	0.440744i	−0.964750	+	0.263169i	$0.915232\pi$
$692$	9.24663			0.351504
$693$		0			0
$694$	15.5829			0.591519
$695$	−24.6261	−	42.6537i	−0.934123	−	1.61795i
$696$		0			0
$697$	−1.42546	+	2.46897i	−0.0539932	+	0.0935189i
$698$	−3.21441	+	5.56751i	−0.121667	+	0.210733i
$699$		0			0
$700$	4.13278	+	7.15818i	0.156204	+	0.270554i
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$		0			0
$703$	19.4720			0.734400
$704$	0.444844	+	0.770492i	0.0167657	+	0.0290390i
$705$		0			0
$706$	3.50821	−	6.07640i	0.132033	−	0.228688i
$707$	−4.76000	+	8.24456i	−0.179018	+	0.310069i
$708$		0			0
$709$	−8.57193	−	14.8470i	−0.321925	−	0.557591i	0.658960	−	0.752178i	$-0.270997\pi$
$709$	−8.57193	−	14.8470i	−0.321925	−	0.557591i	−0.980885	+	0.194587i	$0.937663\pi$
$710$	−0.816630			−0.0306476
$711$		0			0
$712$	28.1245			1.05401
$713$	9.25026	+	16.0219i	0.346425	+	0.600026i
$714$		0			0
$715$	−0.898388	+	1.55605i	−0.0335978	+	0.0581931i
$716$	−12.4540	+	21.5709i	−0.465427	+	0.806143i
$717$		0			0
$718$	−3.31748	−	5.74605i	−0.123807	−	0.214441i
$719$	−43.3519			−1.61675			−0.808377	−	0.588665i	$-0.799654\pi$
$719$	−43.3519			−1.61675			−0.808377	+	0.588665i	$0.799654\pi$
$720$		0			0
$721$	−14.0693			−0.523969
$722$	−4.50666	−	7.80577i	−0.167721	−	0.290501i
$723$		0			0
$724$	7.68759	−	13.3153i	0.285707	−	0.494859i
$725$	0.454762	−	0.787671i	0.0168894	−	0.0292533i
$726$		0			0
$727$	18.1720	+	31.4747i	0.673960	+	1.16733i	0.976772	+	0.214283i	$0.0687415\pi$
$727$	18.1720	+	31.4747i	0.673960	+	1.16733i	−0.302811	+	0.953051i	$0.597925\pi$
$728$	16.7075			0.619220
$729$		0			0
$730$	11.0794			0.410067
$731$	0.0382426	+	0.0662382i	0.00141445	+	0.00244991i
$732$		0			0
$733$	−1.93780	+	3.35637i	−0.0715744	+	0.123970i	−0.899591	−	0.436732i	$-0.856136\pi$
$733$	−1.93780	+	3.35637i	−0.0715744	+	0.123970i	0.828017	+	0.560703i	$0.189469\pi$
$734$	−5.93124	+	10.2732i	−0.218926	+	0.379191i
$735$		0			0
$736$	−19.4997	−	33.7745i	−0.718768	−	1.24494i
$737$	−0.452863			−0.0166814
$738$		0			0
$739$	26.4482			0.972913			0.486456	−	0.873705i	$-0.338289\pi$
$739$	26.4482			0.972913			0.486456	+	0.873705i	$0.338289\pi$
$740$	13.0515	+	22.6058i	0.479782	+	0.831007i
$741$		0			0
$742$	5.17364	−	8.96101i	0.189930	−	0.328969i
$743$	6.73168	−	11.6596i	0.246961	−	0.427750i	−0.715720	−	0.698387i	$-0.753901\pi$
$743$	6.73168	−	11.6596i	0.246961	−	0.427750i	0.962681	+	0.270638i	$0.0872346\pi$
$744$		0			0
$745$	22.3967	+	38.7922i	0.820552	+	1.42124i
$746$	−20.4657			−0.749303
$747$		0			0
$748$	−0.0996320			−0.00364291
$749$	0.307774	+	0.533081i	0.0112458	+	0.0194783i
$750$		0			0
$751$	−1.88415	+	3.26345i	−0.0687537	+	0.119085i	−0.898353	−	0.439274i	$-0.855236\pi$
$751$	−1.88415	+	3.26345i	−0.0687537	+	0.119085i	0.829599	+	0.558359i	$0.188569\pi$
$752$	3.18809	−	5.52194i	0.116258	−	0.201364i
$753$		0			0
$754$	−0.371669	−	0.643750i	−0.0135354	−	0.0234440i
$755$	−39.2536			−1.42859
$756$		0			0
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$	8.06513	+	13.9692i	0.292939	+	0.507385i
$759$		0			0
$760$	−10.3040	+	17.8470i	−0.373764	+	0.647378i
$761$	4.82771	−	8.36185i	0.175005	−	0.303117i	−0.765158	−	0.643842i	$-0.777339\pi$
$761$	4.82771	−	8.36185i	0.175005	−	0.303117i	0.940163	+	0.340725i	$0.110673\pi$
$762$		0			0
$763$	10.1703	+	17.6155i	0.368190	+	0.637724i
$764$	−9.31067			−0.336848
$765$		0			0
$766$	19.1254			0.691030
$767$	−7.80582	−	13.5201i	−0.281852	−	0.488181i
$768$		0			0
$769$	−19.3555	+	33.5247i	−0.697977	+	1.20893i	0.271189	+	0.962526i	$0.412583\pi$
$769$	−19.3555	+	33.5247i	−0.697977	+	1.20893i	−0.969167	+	0.246406i	$0.920750\pi$
$770$	0.655255	−	1.13494i	0.0236138	−	0.0409002i
$771$		0			0
$772$	13.8557	+	23.9989i	0.498679	+	0.863738i
$773$	24.3039			0.874150			0.437075	−	0.899425i	$-0.356014\pi$
$773$	24.3039			0.874150			0.437075	+	0.899425i	$0.356014\pi$
$774$		0			0
$775$	7.08409			0.254468
$776$	19.9612	+	34.5739i	0.716566	+	1.24113i
$777$		0			0
$778$	15.2183	−	26.3589i	0.545603	−	0.945012i
$779$	−13.5305	+	23.4356i	−0.484782	+	0.839666i
$780$		0			0
$781$	−0.0463432	−	0.0802687i	−0.00165829	−	0.00287224i
$782$	−1.57311			−0.0562544
$783$		0			0
$784$	−0.753755			−0.0269198
$785$	1.04955	+	1.81788i	0.0374601	+	0.0648828i
$786$		0			0
$787$	−10.4703	+	18.1351i	−0.373226	+	0.646447i	−0.990060	−	0.140647i	$-0.955082\pi$
$787$	−10.4703	+	18.1351i	−0.373226	+	0.646447i	0.616834	+	0.787094i	$0.288415\pi$
$788$	2.06058	−	3.56904i	0.0734052	−	0.127142i
$789$		0			0
$790$	−0.884738	−	1.53241i	−0.0314776	−	0.0545208i
$791$	−7.41377			−0.263603
$792$		0			0
$793$	−30.9435			−1.09884
$794$	8.15526	+	14.1253i	0.289419	+	0.501289i
$795$		0			0
$796$	−1.53571	+	2.65994i	−0.0544320	+	0.0942789i
$797$	−5.96838	+	10.3375i	−0.211411	+	0.366174i	−0.952156	−	0.305611i	$-0.901139\pi$
$797$	−5.96838	+	10.3375i	−0.211411	+	0.366174i	0.740745	+	0.671786i	$0.234472\pi$
$798$		0			0
$799$	−1.67600	−	2.90291i	−0.0592925	−	0.102698i
$800$	−14.9334			−0.527974
$801$		0			0
$802$	−5.56658			−0.196563
$803$	0.628748	+	1.08902i	0.0221880	+	0.0384308i
$804$		0			0
$805$	−21.8621	+	37.8663i	−0.770538	+	1.33461i
$806$	2.89486	−	5.01404i	0.101967	−	0.176612i
$807$		0			0
$808$	−5.38951	−	9.33490i	−0.189602	−	0.328401i
$809$	8.60808			0.302644			0.151322	−	0.988485i	$-0.451647\pi$
$809$	8.60808			0.302644			0.151322	+	0.988485i	$0.451647\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	−0.572828	−	0.992167i	−0.0201023	−	0.0348182i
$813$		0			0
$814$	0.701018	−	1.21420i	0.0245707	−	0.0425576i
$815$	7.05106	−	12.2128i	0.246988	−	0.427795i
$816$		0			0
$817$	0.363001	+	0.628735i	0.0126998	+	0.0219967i
$818$	8.74141			0.305636
$819$		0			0
$820$	−36.2764			−1.26683
$821$	−14.4881	−	25.0942i	−0.505639	−	0.875793i	−0.999979	−	0.00652409i	$-0.997923\pi$
$821$	−14.4881	−	25.0942i	−0.505639	−	0.875793i	0.494339	−	0.869269i	$-0.335410\pi$
$822$		0			0
$823$	5.62838	−	9.74865i	0.196193	−	0.339816i	−0.751098	−	0.660191i	$-0.770475\pi$
$823$	5.62838	−	9.74865i	0.196193	−	0.339816i	0.947291	+	0.320374i	$0.103809\pi$
$824$	7.96500	−	13.7958i	0.277474	−	0.480599i
$825$		0			0
$826$	5.69331	+	9.86110i	0.198096	+	0.343112i
$827$	30.9279			1.07547			0.537734	−	0.843114i	$-0.319280\pi$
$827$	30.9279			1.07547			0.537734	+	0.843114i	$0.319280\pi$
$828$		0			0
$829$	−9.83524			−0.341592			−0.170796	−	0.985306i	$-0.554634\pi$
$829$	−9.83524			−0.341592			−0.170796	+	0.985306i	$0.554634\pi$
$830$	3.03683	+	5.25994i	0.105410	+	0.182575i
$831$		0			0
$832$	−4.64474	+	8.04493i	−0.161028	+	0.278908i
$833$	−0.198126	+	0.343165i	−0.00686467	+	0.0118900i
$834$		0			0
$835$	12.2383	+	21.1974i	0.423525	+	0.733567i
$836$	−0.945711			−0.0327081
$837$		0			0
$838$	8.07072			0.278798
$839$	6.57160	+	11.3824i	0.226877	+	0.392962i	0.956881	−	0.290481i	$-0.0938151\pi$
$839$	6.57160	+	11.3824i	0.226877	+	0.392962i	−0.730004	+	0.683443i	$0.760482\pi$
$840$		0			0
$841$	14.4370	−	25.0056i	0.497826	−	0.862261i
$842$	−1.24540	+	2.15709i	−0.0429193	+	0.0743383i
$843$		0			0
$844$	17.2619	+	29.8984i	0.594177	+	1.02915i
$845$	16.9873			0.584380
$846$		0			0
$847$	−25.9964			−0.893248
$848$	−1.51552	−	2.62497i	−0.0520433	−	0.0901417i
$849$		0			0
$850$	−0.301182	+	0.521663i	−0.0103305	+	0.0178929i
$851$	−23.3890	+	40.5109i	−0.801763	+	1.38869i
$852$		0			0
$853$	−7.72116	−	13.3734i	−0.264368	−	0.457898i	0.703030	−	0.711160i	$-0.251830\pi$
$853$	−7.72116	−	13.3734i	−0.264368	−	0.457898i	−0.967398	+	0.253262i	$0.918497\pi$
$854$	22.5692			0.772303
$855$		0			0
$856$	−0.696955			−0.0238214
$857$	−10.9914	−	19.0376i	−0.375458	−	0.650312i	0.614937	−	0.788576i	$-0.289181\pi$
$857$	−10.9914	−	19.0376i	−0.375458	−	0.650312i	−0.990395	+	0.138263i	$0.955848\pi$
$858$		0			0
$859$	−9.78334	+	16.9452i	−0.333803	+	0.578164i	−0.983254	−	0.182239i	$-0.941665\pi$
$859$	−9.78334	+	16.9452i	−0.333803	+	0.578164i	0.649451	+	0.760403i	$0.274999\pi$
$860$	−0.486616	+	0.842844i	−0.0165935	+	0.0287408i
$861$		0			0
$862$	−11.2495	−	19.4846i	−0.383158	−	0.663649i
$863$	21.8676			0.744383			0.372191	−	0.928156i	$-0.378607\pi$
$863$	21.8676			0.744383			0.372191	+	0.928156i	$0.378607\pi$
$864$		0			0
$865$	18.7298			0.636833
$866$	7.82495	+	13.5532i	0.265903	+	0.460557i
$867$		0			0
$868$	4.46164	−	7.72779i	0.151438	−	0.262298i
$869$	0.100416	−	0.173926i	0.00340640	−	0.00590005i
$870$		0			0
$871$	−2.36424	−	4.09498i	−0.0801092	−	0.138753i
$872$	−23.0307			−0.779918
$873$		0			0
$874$	−14.9320			−0.505084
$875$	−7.96850	−	13.8019i	−0.269385	−	0.466588i
$876$		0			0
$877$	19.5499	−	33.8615i	0.660155	−	1.14342i	−0.320420	−	0.947276i	$-0.603824\pi$
$877$	19.5499	−	33.8615i	0.660155	−	1.14342i	0.980575	−	0.196146i	$-0.0628426\pi$
$878$	5.86300	−	10.1550i	0.197867	−	0.342715i
$879$		0			0
$880$	−0.191945	−	0.332459i	−0.00647047	−	0.0112072i
$881$	−7.30508			−0.246115			−0.123057	−	0.992400i	$-0.539270\pi$
$881$	−7.30508			−0.246115			−0.123057	+	0.992400i	$0.539270\pi$
$882$		0			0
$883$	−3.49293			−0.117546			−0.0587732	−	0.998271i	$-0.518719\pi$
$883$	−3.49293			−0.117546			−0.0587732	+	0.998271i	$0.518719\pi$
$884$	−0.520144	−	0.900916i	−0.0174943	−	0.0303011i
$885$		0			0
$886$	7.35639	−	12.7416i	0.247143	−	0.428064i
$887$	−14.2106	+	24.6136i	−0.477147	+	0.826442i	−0.999657	−	0.0261907i	$-0.991662\pi$
$887$	−14.2106	+	24.6136i	−0.477147	+	0.826442i	0.522510	+	0.852633i	$0.324996\pi$
$888$		0			0
$889$	21.9317	+	37.9868i	0.735564	+	1.27404i
$890$	23.0340			0.772102
$891$		0			0
$892$	5.20125			0.174151
$893$	−15.9086	−	27.5546i	−0.532362	−	0.922078i
$894$		0			0
$895$	−25.2266	+	43.6937i	−0.843231	+	1.46052i
$896$	−10.4684	+	18.1317i	−0.349724	+	0.605739i
$897$		0			0
$898$	5.55434	+	9.62039i	0.185351	+	0.321037i
$899$	−0.981898			−0.0327481
$900$		0			0
$901$	−1.59344			−0.0530851
$902$	0.974234	+	1.68742i	0.0324384	+	0.0561850i
$903$		0			0
$904$	4.19712	−	7.26962i	0.139594	−	0.241784i
$905$	15.5719	−	26.9713i	0.517626	−	0.896555i
$906$		0			0
$907$	−26.5583	−	46.0004i	−0.881855	−	1.52742i	−0.849276	−	0.527949i	$-0.822961\pi$
$907$	−26.5583	−	46.0004i	−0.881855	−	1.52742i	−0.0325791	−	0.999469i	$-0.510372\pi$
$908$	−3.41560			−0.113351
$909$		0			0
$910$	13.6834			0.453601
$911$	4.03794	+	6.99392i	0.133783	+	0.231719i	0.925132	−	0.379646i	$-0.123954\pi$
$911$	4.03794	+	6.99392i	0.133783	+	0.231719i	−0.791349	+	0.611365i	$0.790621\pi$
$912$		0			0
$913$	−0.344675	+	0.596995i	−0.0114071	+	0.0197577i
$914$	7.07273	−	12.2503i	0.233945	−	0.405205i
$915$		0			0
$916$	−10.8195	−	18.7398i	−0.357485	−	0.619182i
$917$	33.8116			1.11656
$918$		0			0
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$	−24.7534	−	42.8741i	−0.816095	−	1.41352i
$921$		0			0
$922$	10.2748	−	17.7965i	0.338382	−	0.586095i
$923$	0.483883	−	0.838110i	0.0159272	−	0.0275867i
$924$		0			0
$925$	8.95593	+	15.5121i	0.294469	+	0.510036i
$926$	−14.7060			−0.483268
$927$		0			0
$928$	2.06986			0.0679464
$929$	14.4970	+	25.1095i	0.475630	+	0.823815i	0.999610	−	0.0279151i	$-0.00888679\pi$
$929$	14.4970	+	25.1095i	0.475630	+	0.823815i	−0.523980	+	0.851730i	$0.675553\pi$
$930$		0			0
$931$	−1.88062	+	3.25734i	−0.0616350	+	0.106755i
$932$	19.0928	−	33.0697i	0.625406	−	1.08324i
$933$		0			0
$934$	−6.51715	−	11.2880i	−0.213248	−	0.369356i
$935$	−0.201813			−0.00659999
$936$		0			0
$937$	5.02850			0.164274			0.0821369	−	0.996621i	$-0.473826\pi$
$937$	5.02850			0.164274			0.0821369	+	0.996621i	$0.473826\pi$
$938$	1.72440	+	2.98675i	0.0563037	+	0.0975208i
$939$		0			0
$940$	21.3261	−	36.9380i	0.695582	−	1.20478i
$941$	27.9205	−	48.3598i	0.910183	−	1.57648i	0.0963791	−	0.995345i	$-0.469274\pi$
$941$	27.9205	−	48.3598i	0.910183	−	1.57648i	0.813804	−	0.581139i	$-0.197393\pi$
$942$		0			0
$943$	−32.5046	−	56.2997i	−1.05850	−	1.83337i
$944$	3.33551			0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	−21.2647	−	36.8315i	−0.691009	−	1.19686i	−0.971508	−	0.237009i	$-0.923833\pi$
$947$	−21.2647	−	36.8315i	−0.691009	−	1.19686i	0.280498	−	0.959855i	$-0.409500\pi$
$948$		0			0
$949$	−6.56494	+	11.3708i	−0.213107	+	0.369112i
$950$	−2.85884	+	4.95165i	−0.0927529	+	0.160653i
$951$		0			0
$952$	0.938287	+	1.62516i	0.0304101	+	0.0526718i
$953$	21.8148			0.706651			0.353325	−	0.935501i	$-0.385051\pi$
$953$	21.8148			0.706651			0.353325	+	0.935501i	$0.385051\pi$
$954$		0			0
$955$	−18.8595			−0.610280
$956$	−9.98196	−	17.2893i	−0.322840	−	0.559174i
$957$		0			0
$958$	−3.79592	+	6.57472i	−0.122640	+	0.212419i
$959$	23.3947	−	40.5208i	0.755454	−	1.30848i
$960$		0			0
$961$	11.6761	+	20.2236i	0.376648	+	0.652374i
$962$	14.6391			0.471983
$963$		0			0
$964$	−11.4618			−0.369158
$965$	28.0660	+	48.6117i	0.903476	+	1.56487i
$966$		0			0
$967$	−2.31429	+	4.00847i	−0.0744227	+	0.128904i	−0.900835	−	0.434161i	$-0.857045\pi$
$967$	−2.31429	+	4.00847i	−0.0744227	+	0.128904i	0.826412	+	0.563065i	$0.190378\pi$
$968$	14.7172	−	25.4910i	0.473030	−	0.819312i
$969$		0			0
$970$	16.3483	+	28.3160i	0.524911	+	0.909173i
$971$	−21.6509			−0.694809			−0.347405	−	0.937715i	$-0.612937\pi$
$971$	−21.6509			−0.694809			−0.347405	+	0.937715i	$0.612937\pi$
$972$		0			0
$973$	−42.5714			−1.36478
$974$	−0.187383	−	0.324556i	−0.00600413	−	0.0103995i
$975$		0			0
$976$	3.30562	−	5.72551i	0.105810	−	0.183269i
$977$	11.0424	−	19.1260i	0.353278	−	0.611895i	−0.633544	−	0.773707i	$-0.718400\pi$
$977$	11.0424	−	19.1260i	0.353278	−	0.611895i	0.986822	+	0.161812i	$0.0517337\pi$
$978$		0			0
$979$	1.30716	+	2.26407i	0.0417771	+	0.0723601i
$980$	−5.04210			−0.161064
$981$		0			0
$982$	−20.0758			−0.640646
$983$	6.93152	+	12.0058i	0.221081	+	0.382924i	0.955137	−	0.296166i	$-0.0957081\pi$
$983$	6.93152	+	12.0058i	0.221081	+	0.382924i	−0.734055	+	0.679090i	$0.762375\pi$
$984$		0			0
$985$	4.17389	−	7.22938i	0.132991	−	0.230347i
$986$	0.0417457	−	0.0723057i	0.00132946	−	0.00230268i
$987$		0			0
$988$	−4.93723	−	8.55153i	−0.157074	−	0.272060i
$989$	−1.74408			−0.0554587
$990$		0			0
$991$	34.8224			1.10617			0.553084	−	0.833125i	$-0.313451\pi$
$991$	34.8224			1.10617			0.553084	+	0.833125i	$0.313451\pi$
$992$	8.06084	+	13.9618i	0.255932	+	0.443287i
$993$		0			0
$994$	−0.352928	+	0.611290i	−0.0111942	+	0.0193889i
$995$	−3.11072	+	5.38792i	−0.0986164	+	0.170809i
$996$		0			0
$997$	12.3749	+	21.4339i	0.391916	+	0.678819i	0.992702	−	0.120591i	$-0.0384789\pi$
$997$	12.3749	+	21.4339i	0.391916	+	0.678819i	−0.600786	+	0.799410i	$0.705146\pi$
$998$	11.2488			0.356073
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.e.244.4		12
3.2	odd	2		729.2.c.b.244.3		12
9.2	odd	6		729.2.c.b.487.3		12
9.4	even	3		729.2.a.a.1.3		6
9.5	odd	6		729.2.a.d.1.4		6
9.7	even	3	inner	729.2.c.e.487.4		12
27.2	odd	18		243.2.e.b.28.2		12
27.4	even	9		243.2.e.c.217.1		12
27.5	odd	18		81.2.e.a.19.1		12
27.7	even	9		27.2.e.a.4.2	✓	12
27.11	odd	18		243.2.e.a.109.2		12
27.13	even	9		243.2.e.d.136.1		12
27.14	odd	18		243.2.e.a.136.2		12
27.16	even	9		243.2.e.d.109.1		12
27.20	odd	18		81.2.e.a.64.1		12
27.22	even	9		27.2.e.a.7.2	yes	12
27.23	odd	18		243.2.e.b.217.2		12
27.25	even	9		243.2.e.c.28.1		12
108.7	odd	18		432.2.u.c.193.2		12
108.103	odd	18		432.2.u.c.385.2		12
135.7	odd	36		675.2.u.b.274.2		24
135.22	odd	36		675.2.u.b.574.3		24
135.34	even	18		675.2.l.c.301.1		12
135.49	even	18		675.2.l.c.601.1		12
135.88	odd	36		675.2.u.b.274.3		24
135.103	odd	36		675.2.u.b.574.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	27.7	even	9
27.2.e.a.7.2	yes	12	27.22	even	9
81.2.e.a.19.1		12	27.5	odd	18
81.2.e.a.64.1		12	27.20	odd	18
243.2.e.a.109.2		12	27.11	odd	18
243.2.e.a.136.2		12	27.14	odd	18
243.2.e.b.28.2		12	27.2	odd	18
243.2.e.b.217.2		12	27.23	odd	18
243.2.e.c.28.1		12	27.25	even	9
243.2.e.c.217.1		12	27.4	even	9
243.2.e.d.109.1		12	27.16	even	9
243.2.e.d.136.1		12	27.13	even	9
432.2.u.c.193.2		12	108.7	odd	18
432.2.u.c.385.2		12	108.103	odd	18
675.2.l.c.301.1		12	135.34	even	18
675.2.l.c.601.1		12	135.49	even	18
675.2.u.b.274.2		24	135.7	odd	36
675.2.u.b.274.3		24	135.88	odd	36
675.2.u.b.574.2		24	135.103	odd	36
675.2.u.b.574.3		24	135.22	odd	36
729.2.a.a.1.3		6	9.4	even	3
729.2.a.d.1.4		6	9.5	odd	6
729.2.c.b.244.3		12	3.2	odd	2
729.2.c.b.487.3		12	9.2	odd	6
729.2.c.e.244.4		12	1.1	even	1	trivial
729.2.c.e.487.4		12	9.7	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(0.400763 + 0.694143i) q^{2} +(0.678777 - 1.17568i) q^{4} +(1.37492 - 2.38143i) q^{5} +(-1.18842 - 2.05840i) q^{7} +2.69117 q^{8} +O(q^{10})\)	\(q+(0.400763 + 0.694143i) q^{2} +(0.678777 - 1.17568i) q^{4} +(1.37492 - 2.38143i) q^{5} +(-1.18842 - 2.05840i) q^{7} +2.69117 q^{8} +2.20407 q^{10} +(0.125079 + 0.216644i) q^{11} +(-1.30599 + 2.26204i) q^{13} +(0.952548 - 1.64986i) q^{14} +(-0.279032 - 0.483297i) q^{16} -0.293377 q^{17} -2.78475 q^{19} +(-1.86653 - 3.23292i) q^{20} +(-0.100255 + 0.173646i) q^{22} +(3.34492 - 5.79357i) q^{23} +(-1.28081 - 2.21843i) q^{25} -2.09357 q^{26} -3.22668 q^{28} +(0.177529 + 0.307488i) q^{29} +(-1.38273 + 2.39496i) q^{31} +(2.91482 - 5.04862i) q^{32} +(-0.117575 - 0.203645i) q^{34} -6.53592 q^{35} -6.99238 q^{37} +(-1.11602 - 1.93301i) q^{38} +(3.70015 - 6.40884i) q^{40} +(4.85880 - 8.41569i) q^{41} +(-0.130353 - 0.225778i) q^{43} +0.339604 q^{44} +5.36209 q^{46} +(5.71278 + 9.89482i) q^{47} +(0.675331 - 1.16971i) q^{49} +(1.02661 - 1.77813i) q^{50} +(1.77295 + 3.07085i) q^{52} +5.43137 q^{53} +0.687897 q^{55} +(-3.19823 - 5.53950i) q^{56} +(-0.142294 + 0.246460i) q^{58} +(-2.98846 + 5.17617i) q^{59} +(5.92338 + 10.2596i) q^{61} -2.21660 q^{62} +3.55649 q^{64} +(3.59127 + 6.22026i) q^{65} +(-0.905151 + 1.56777i) q^{67} +(-0.199138 + 0.344916i) q^{68} +(-2.61936 - 4.53686i) q^{70} -0.370510 q^{71} +5.02679 q^{73} +(-2.80229 - 4.85371i) q^{74} +(-1.89022 + 3.27396i) q^{76} +(0.297293 - 0.514927i) q^{77} +(-0.401411 - 0.695264i) q^{79} -1.53459 q^{80} +7.78892 q^{82} +(1.37783 + 2.38646i) q^{83} +(-0.403370 + 0.698657i) q^{85} +(0.104482 - 0.180967i) q^{86} +(0.336610 + 0.583026i) q^{88} +10.4507 q^{89} +6.20825 q^{91} +(-4.54091 - 7.86509i) q^{92} +(-4.57895 + 7.93097i) q^{94} +(-3.82880 + 6.63168i) q^{95} +(7.41730 + 12.8471i) q^{97} +1.08259 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 + 6 * q^10 + 12 * q^11 + 6 * q^14 + 3 * q^16 - 18 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 15 * q^23 + 6 * q^25 - 30 * q^26 - 12 * q^28 + 12 * q^29 - 24 * q^35 + 6 * q^37 - 3 * q^38 - 6 * q^40 + 15 * q^41 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 12 * q^49 + 3 * q^50 - 12 * q^52 - 18 * q^53 - 12 * q^55 - 6 * q^56 + 12 * q^58 + 24 * q^59 + 9 * q^61 + 24 * q^62 - 24 * q^64 - 6 * q^65 + 9 * q^67 - 9 * q^68 - 15 * q^70 - 54 * q^71 - 12 * q^73 - 12 * q^74 - 6 * q^76 - 12 * q^77 + 42 * q^80 - 12 * q^82 + 12 * q^83 - 21 * q^86 - 12 * q^88 - 18 * q^89 - 12 * q^91 + 6 * q^92 - 6 * q^94 + 12 * q^95 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more